Pollack, P (2023)

Two Problems on the Distribution of Carmichael’s Lambda Function

Preprint.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

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Abstract: Let λ(n) denote the exponent of the multiplicative group modulo n. We show that when q is odd, each coprime residue class modulo q is hit equally often by λ(n) as n varies. Under the stronger assumption that gcd(q, 6) = 1, we prove that equidistribution persists throughout a Siegel–Wal sz-type range of uniformity. By similar methods we show that λ(n) obeys Benford’s leading digit law with respect to natural density. Moreover, if we assume GRH, then Benford’s law holds for the order of a mod n, for any xed integer a ∈/ {0, ±1}.

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Bibtex:
@misc{, author = {Paul Pollack}, title = {Two Problems on the Distribution of Carmichael’s Lambda Function}, year = {2023}, url = {http://pollack.uga.edu/lambdadist2.pdf}, }

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Reference Type: Preprint

Subject Area(s): Number Theory

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