On Benford’s law for multiplicative functions

On Benford’s law for multiplicative functions

We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the k-divisor functions, where k \neq 10^j, and Hecke eigenvalues of newforms, such as Ramanujan tau function, are strong Benford. In contrast to some earlier work, our...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-11, Vol.151 (11), p.4607-4619
Hauptverfasser: Chandee, Vorrapan, Li, Xiannan, Pollack, Paul, Singha Roy, Akash
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the k-divisor functions, where k \neq 10^j, and Hecke eigenvalues of newforms, such as Ramanujan tau function, are strong Benford. In contrast to some earlier work, our approach is based on Halász’s Theorem.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/16480