Cross Reference Up

Kuipers, L and Niederreiter, H (1974). Uniform Distribution of Sequences. J. Wiley; newer edition - 2006 from Dover.

This work is cited by the following items of the Benford Online Bibliography:

Note that this list may be incomplete, and is currently being updated. Please check again at a later date.

Anderson, TC, Rolen, L and Stoehr, R (2011). Benford's Law for Coefficients of Modular Forms and Partition Functions. Proceedings of the American Mathematical Society, Vol. 139, No. 5, May 2011, pp. 1533-1541. ISSN/ISBN:0002-9939. View Complete Reference Online information Works that this work references Works that reference this work
Baláž, V, Nagasaka, K and Strauch, O (2010). Benford's law and distribution functions of sequences in (0, 1). Mathematical Notes, 2010, Vol. 88, No. 4, pp 449–463. Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 4, pp. 485–501. ISSN/ISBN:0001-4346. DOI:10.1134/S0001434610090178. View Complete Reference Online information Works that this work references Works that reference this work
Baumeister, J and Macedo, TG (2011). Von den Zufallszahlen und ihrem Gebrauch. Stand: 21, November 2011. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Becker, T, Burt, D, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J, Strauch, FW and Talbut, B (2018). Benford's Law and Continuous Dependent Random Variables. Annals of Physics 388, pp. 350–381. DOI:10.1016/j.aop.2017.11.013. View Complete Reference Online information Works that this work references Works that reference this work
Becker, T, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J and Strauch, FW (2013). Benford's Law and Continuous Dependent Random Variables. Preprint arXiv:1309.5603 [math.PR]; last accessed October 23, 2018. DOI:10.1016/j.aop.2017.11.013. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Benford’s Law in power-like dynamical systems. Stochastics and Dynamics 5, pp. 587-607. ISSN/ISBN:0219-4937. DOI:10.1142/S0219493705001602. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Multi-dimensional dynamical systems and Benford's law. Discrete and Continuous Dynamical Systems 13(1), pp. 219-237. ISSN/ISBN:1078-0947. DOI:10.3934/dcds.2005.13.219. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Dynamics and digits: on the ubiquity of Benford’s law. In: F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel (eds): Proceedings of Equadiff 2003. World Scientific, pp. 693-695. DOI:10.1142/9789812702067_0115 . View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), pp. 137-159. DOI:10.1080/10236198.2010.549012. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2015). Most linear flows on ℝ^d are Benford . Journal of Differential Equations 259(5), pp. 1933–1957. DOI:10.1016/j.jde.2015.03.016. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), pp. 197-219. ISSN/ISBN:0002-9947. DOI:10.1090/S0002-9947-04-03455-5. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Eshun, G (2014). Benford solutions of linear difference equations. Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics Volume 102, pp. 23-60. ISSN/ISBN:978-3-662-44139-8. DOI:10.1007/978-3-662-44140-4_2. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Eshun, G (2016). A characterization of Benford's law in discrete-time linear systems. Journal of Dynamics and Differential Equations 28(2), pp. 432-469. ISSN/ISBN:1040-7294. DOI:10.1007/s10884-014-9393-y. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Evans, SN (2013). A Limit Theorem for Occupation Measures of Lévy Processes in Compact Groups. Stochastics and Dynamics 13(1), p. 1250008. DOI:10.1142/S0219493712500086. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, pp. 1-126. DOI:10.1214/11-PS175. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Hill, TP (2015). An Introduction to Benford's Law. Princeton University Press: Princeton, NJ. ISSN/ISBN:9780691163062. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A, Hill, TP, Kaynar, B and Ridder, A (2011). Finite-state Markov Chains Obey Benford's Law. SIAM Journal of Matrix Analysis and Applications 32(3), pp. 665-684. DOI:10.1137/100789890. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Siegmund, S (2007). On the distribution of mantissae in nonautonomous difference equations. Journal of Difference Equations and Applications 13(8-9), pp. 829-845. ISSN/ISBN:1023-6198. DOI:10.1080/10236190701388039. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2017). Leading Digits of Mersenne Numbers. Preprint in arXiv:1712.04425 [math.NT]; last accessed October 23, 2018. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2019). The Surprising Accuracy of Benford’s Law in Mathematics. Preprint arXiv:1907.08894 [math.PR]; last accessed July 31, 2019. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2020). The Surprising Accuracy of Benford’s Law in Mathematics. The American Mathematical Monthly 127(3), pp. 217-237. DOI:10.1080/00029890.2020.1690387. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2021). Leading digits of Mersenne numbers. Experimental Mathematics 30(3), pp. 405–421. DOI:10.1080/10586458.2018.1551162. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Hildebrand, AJ and Li, J (2018). A local Benford Law for a class of arithmetic sequences. Preprint arXiv:1808.01496 [math.NT]; last accessed October 22, 2018. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Hildebrand, AJ and Li, J (2019). A local Benford law for a class of arithmetic sequences. International Journal of Number Theory 15(3), pp.613-638. DOI:10.1142/S1793042119500325. View Complete Reference Online information Works that this work references Works that reference this work
Chenavier, N, Massé, B and Schneider, D (2018). Products of random variables and the first digit phenomenon. Preprint arXiv:1512.06049 [math.PR]; last accessed January 9, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Chenavier, N and Schneider, D (2018). On the discrepancy of powers of random variables. Statistics & Probability Letters 134, pp. 5-14. DOI:10.1016/j.spl.2017.10.006. View Complete Reference Online information Works that this work references Works that reference this work
Cohen, DIA and Katz, TM (1984). Prime Numbers and the First Digit Phenomenon. Journal of Number Theory 18(3), pp. 261-268. ISSN/ISBN:0022-314X. DOI:10.1016/0022-314X(84)90061-1. View Complete Reference Online information Works that this work references Works that reference this work
Cuenca, AV (2023). La Ley de Benford, Del Primer Dígito Significativo. Trabajo Fin de Grado en Matemáticas, Universidad de Valladolid . SPA View Complete Reference Online information Works that this work references No Bibliography works reference this work
Deligny, H and Jolissaint, P (2012). Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]. Elemente der Mathematik, 68(1), pp. 9-21. DOI:10.4171/EM/213. FRE View Complete Reference Online information Works that this work references Works that reference this work
Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), pp. 72-81. ISSN/ISBN:0091-1798. View Complete Reference Online information Works that this work references Works that reference this work
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651. View Complete Reference Online information Works that this work references Works that reference this work
Eliahou, S, Massé, B and Schneider, D (2013). On the mantissa distribution of powers of natural and prime numbers. Acta Mathematica Hungarica, 139(1), pp. 49-63. ISSN/ISBN:0236-5294. DOI:10.1007/s10474-012-0244-1. View Complete Reference Online information Works that this work references Works that reference this work
Fisher, AM and Zhang, X (2023). Uniform distribution mod 1 for sequences of ergodic sums and continued fractions. Preprint arXiv:2307.14843 [math.DS]; last accessed August 5, 2023 . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Giuliano, R (2011). Weak convergence of sequences from fractional parts of random variables and applications. Theory of Probability and Mathematical Statistics 83, pp. 59-69. DOI:10.1090/S0094-9000-2012-00841-7 . View Complete Reference Online information Works that this work references Works that reference this work
Giuliano-Antonini, R (1991). On the notion of uniform distribution mod 1. Fibonacci Quarterly 29(3), pp. 230-234. View Complete Reference Online information Works that this work references Works that reference this work
Golafshan, M and Mitrofanov, I (2024). Complexity function of the most significant digits of 2ND. arXiv:2402.16210. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Goto, K (1992). Some examples of Benford sequences. Mathematical Journal of the Okayama University 34, pp. 225-232. View Complete Reference Online information Works that this work references Works that reference this work
Goto, K and Kano, T (1985). Uniform distribution of some special sequences. Proc. Japan Acad. Ser. A Math. Sci. 61(3), pp. 83-86. View Complete Reference Online information Works that this work references Works that reference this work
Hürlimann, W (2003). A generalized Benford law and its application. Advances and Applications in Statistics 3(3), pp. 217-228. View Complete Reference Online information Works that this work references Works that reference this work
Hürlimann, W (2004). Integer powers and Benford’s law. International Journal of Pure and Applied Mathematics 11(1), pp. 39-46. View Complete Reference No online information available Works that this work references Works that reference this work
Iyengar, SS, Rajagopal, AK and Uppuluri, VRR (1983). String Patterns of Leading Digits. Applied Mathematics and Computation 12(4), pp. 321-337. ISSN/ISBN:0096-3003. DOI:10.1016/0096-3003(83)90045-0. View Complete Reference Online information Works that this work references Works that reference this work
Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG. View Complete Reference Online information Works that this work references Works that reference this work
Jolissaint, P (2009). Loi de Benford, relations de récurrence et suites équidistribuées II. Elem. Math. 64 (1), pp. 21-36. FRE View Complete Reference Online information Works that this work references Works that reference this work
Kanemitsu, S, Nagasaka, K, Rauzy, G and Shiue, JS (1988). On Benford’s law: the first digit problem. Lecture Notes in Mathematics 1299, pp. 158-169 (eds. Watanabe, S, and Prokhorov, YV). ISSN/ISBN:978-3-540-18814-8. DOI:10.1007/BFb0078471. View Complete Reference Online information Works that this work references Works that reference this work
Kontorovich, AV and Miller, SJ (2005). Benford's Law, Values of L-functions and the 3x+ 1 Problem. Acta Arithmetica 120(3), pp. 269-297. ISSN/ISBN:0065-1036. DOI:10.4064/aa120-3-4. View Complete Reference Online information Works that this work references Works that reference this work
Kozlov, VV (2005). Weighted averages, uniform distribution, and strict ergodicity. Russian Mathematical Surveys 60(6), pp. 1121-1146. ISSN/ISBN:0036-0279. DOI:10.1070/RM2005v060n06ABEH004284. View Complete Reference Online information Works that this work references Works that reference this work
Kunoff, S (1987). N! has the first digit property. Fibonacci Quarterly 25, pp. 365-367. View Complete Reference No online information available Works that this work references Works that reference this work
Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, pp. 289-303. ISSN/ISBN:0024-6107. DOI:10.1112/S0024610706023131. View Complete Reference Online information Works that this work references Works that reference this work
Massé, B (2021). Random walks on the circle and measure of irrationality. Research Report, Université du littoral côte d'Opale. View Complete Reference Online information Works that this work references Works that reference this work
Massé, B (2021). Random subsequences of αn with asymptotically independent successive terms. Research Report, Université du Littoral - Côte d'Opale. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Massé, B and Schneider, D (2011). A survey on weighted densities and their connection with the first digit phenomenon. Rocky Mountain Journal of Mathematics 41(5), 1395-1415. ISSN/ISBN:0035-7596. DOI:10.1216/RMJ-2011-41-5-1395. View Complete Reference Online information Works that this work references Works that reference this work
Massé, B and Schneider, D (2012). Random number sequences and the first digit phenomenon. Electronic Journal of Probability, Vol 17, Article 86, pp. 1-17 . DOI:10.1214/EJP.v17-1900. View Complete Reference Online information Works that this work references Works that reference this work
Massé, B and Schneider, D (2014). The mantissa distribution of the primorial numbers. Acta Arithmetica 163, pp. 45-58. ISSN/ISBN:0065-1036. DOI:10.4064/aa163-1-4. View Complete Reference Online information Works that this work references Works that reference this work
Massé, B and Schneider, D (2015). Fast growing sequences of numbers and the first digit phenomenon . International Journal of Number Theory 11:705, pp. 705--719. DOI:10.1142/S1793042115500384. View Complete Reference Online information Works that this work references Works that reference this work
McLaughlin, WI and Lundy, SA (1984). Digit functions of integer sequences. Fibonacci Quarterly 22(2), pp. 105-115. ISSN/ISBN:0015-0517. View Complete Reference Online information Works that this work references Works that reference this work
Miller, SJ and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. ISSN/ISBN:978-0691120607. View Complete Reference Online information Works that this work references Works that reference this work
Miller, SJ and Takloo-Bighash, R (2007). Introduction to Random Matrix Theory. In: An Invitation to Modern Number Theory, Princeton University Press. ISSN/ISBN:9780691120607. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Miller, SJ (ed.) (2015). Benford's Law: Theory and Applications. Princeton University Press: Princeton and Oxford. ISSN/ISBN:978-0-691-14761-1. View Complete Reference Online information Works that this work references Works that reference this work
Mori, Y and Takashima, K (2016). On the distribution of the leading digit of an: a study via 𝜒2 statistics. Period. Math. Hungar. 73(2), 224-239. ISSN/ISBN:0031-5303. DOI:10.1007/s10998-016-0138-z. View Complete Reference Online information Works that this work references Works that reference this work
Nagasaka, K (1984). On Benford's Law. Annals of the Institute of Statistical Mathematics 36(2), pp. 337-352. ISSN/ISBN:0020-3157. DOI:10.1007/BF02481974. View Complete Reference Online information Works that this work references Works that reference this work
Nagasaka, K, Kanemitsu, S and Shiue, JS (1990). Benford’s law: The logarithmic law of first digit. In: Győry, K, Halász, G. (eds.) Number theory. Vol. I. Elementary and analytic, Proc. Conf., Budapest/Hung. 1987, Colloq. Math. Soc. János Bolyai 51, pp. 361-391 . View Complete Reference No online information available Works that this work references Works that reference this work
Nagasaka, K and Shiue, JS (1987). Benford's law for linear recurrence sequences. Tsukuba Journal of Mathematics 11(2), pp. 341-351. View Complete Reference No online information available Works that this work references Works that reference this work
Ohkubo, Y and Strauch, O (2019). Distribution of leading digits of numbers II. Uniform Distribution Theory 14(1), pp. 19-42. DOI:10.2478/udt-2019–0003. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Patterson, C and Scheepers, M (2024). Benford's Law in the ring ℤ(√ D). arXiv:2402.10864 . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Posch, PN (2005). Ziffernanalyse in Theorie und Praxis. Testverfahren zur Fälschungsaufspürung mit Benfords Gesetz. Diploma thesis, Universität Bonn, Germany, 2003. Published by Shaker Verlag, Aachen. GER View Complete Reference No online information available Works that this work references Works that reference this work
Posch, PN (2008). A Survey on Sequences and Distribution Functions satisfying the First-Digit-Law. Journal of Statistics & Management Systems 11(1), pp. 1-19. DOI:10.1080/09720510.2008.10701294. View Complete Reference Online information Works that this work references Works that reference this work
Posch, PN (2010). Ziffernanalyse mit dem Newcomb-Benford Gesetz in Theorie und Praxis. VEW Verlag Europäische Wirtschaft: Munich 2nd edition. GER View Complete Reference Online information Works that this work references Works that reference this work
Rahmatidehkordi, A (2023). Probability Distributions on a Circle. Master of Science Thesis, Department of Mathematical and Statistical Sciences, University of Alberta. DOI:10.7939/r3-85pm-r259. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), pp. 521-538. ISSN/ISBN:0002-9890. DOI:10.2307/2319349. View Complete Reference Online information Works that this work references Works that reference this work
Ravikumar, B (2008). The Benford-Newcomb Distribution and Unambiguous Context-Free Languages. International Journal of Foundations of Computer Science 19(3), pp. 717-727. ISSN/ISBN:0129-0541. DOI:10.1142/S0129054108005905. View Complete Reference Online information Works that this work references Works that reference this work
Ravikumar, B (2009). A simple multiplication game and its analysis. Accepted for publication in the International Journal of Combinatorial Number Theory. View Complete Reference Online information Works that this work references Works that reference this work
Romano, PK and McLaughlin, H (2011). On non-linear recursive sequences and Benford’s Law. Fibonacci Quarterly 49(2), pp. 134–138. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1983). On sums modulo 2π of independent random variables. Math. Nachr. 110, 243-262. DOI:10.1002/mana.19831100118. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1983). On H∞ -summability and the uniform distribution of sequences. Math. Nachr. 113, 237-243. DOI:10.1002/mana.19831130122. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1987). Some estimates of the H∞ -uniform distribution. Monatshefte für Mathematik 103, 233-240. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. ISSN/ISBN:0863-0593. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1988). On the uniform distribution of certain sequences and Benford’s law. Math. Nachr. 136, 271-273. DOI:10.1002/mana.19881360119. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1988). On a law of the iterated logarithm for sums mod 1 with application to Benford's law. Probability Theory and Related Fields 77(2), 167-178. ISSN/ISBN:0178-8051. DOI:10.1007/BF00334035. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1989). On measures of uniformly distributed sequences and Benford's law. Monatshefte für Mathematik 107(3), 245-256. ISSN/ISBN:0026-9255. DOI:10.1007/BF01300347. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1990). On Benford’s law for continued fractions. Math. Nachr. 148, 137-144. DOI:10.1002/mana.3211480108. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1991). On a uniform law of the iterated logarithm for sums mod 1 and Benford’s law. Lithuanian Mathematical Journal 31(1), 133-142. DOI:10.1007/BF00972327. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN/ISBN:0167-7152. DOI:10.1016/S0167-7152(97)00142-9. View Complete Reference Online information Works that this work references Works that reference this work
Strauch, O (2012). Unsolved Problems. Uniform Distribution Theory, Unsolved Problems Section on the home-page of Uniform Distribution Theory. ISSN/ISBN:1336-913X. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Tichy, RF (1985). Uniform distribution and diophantine inequalities. Monatsh. Math. 99(2), 147-152. ISSN/ISBN:0026-9255. DOI:10.1007/BF01304194. View Complete Reference Online information Works that this work references Works that reference this work
Tichy, RF (1987). Gleichverteilung zum Summierungsverfahren H∞. Math. Nachr. 131(1), 119-125. DOI:10.1002/mana.19871310112. GER View Complete Reference Online information Works that this work references Works that reference this work
Tichy, RF (1987). Statistische Resultate über computergerechte Darstellungen von Zahlen. Anzeiger der Österreichischen Akademie der Wissenschaften. Mathematisch- Naturwissenschaftliche Klasse 124, pp.1-8. GER View Complete Reference No online information available Works that this work references Works that reference this work
Too, YH (1992). On the uniform distribution modulo one of some log-like sequences. Proc. Japan Acad. A 68, 269-272. View Complete Reference Online information Works that this work references Works that reference this work
Uhlig, N (2016). Rundum das Benfordsche Gesetz. Diploma thesis, University of Leipzig, Fakultät für Mathematik und Informatik. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Volcic, A (2020). Uniform distribution, Benford’s law and scale-invariance. Bollettino dell'Unione Matematica Italiana. DOI:10.1007/s40574-020-00245-6. View Complete Reference Online information Works that this work references Works that reference this work
Wilms, RJG and Brands, JJAM (1994). On the asymptotically uniform distribution modulo 1 of extreme order statistics. Statistica Neerlandica 48(1), 63-70. DOI:10.1111/j.1467-9574.1994.tb01431.x. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Zheng, S (2013). Necessary and Sufficient Conditions for Benford Sequences. Pi Mu Epsilon Journal 13(9), pp. 553 – 561. View Complete Reference Online information Works that this work references Works that reference this work