On Benford’s law for multiplicative functions
Copyright policy )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 k -divisor functions, where k ≠ 10 j 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.
- University of Georgia Research Foundation Inc United States
- Kansas State University United States
- University of Georgia Press United States
Halász's theorem, uniformly distribution modulo 1, Mathematics - Number Theory, Weyl's criterion, Sequences and sets, Primes, Distribution functions associated with additive and positive multiplicative functions, divisor functions, multiplicative functions, Euler's function, FOS: Mathematics, Hecke eigenvalues of new forms, Number Theory (math.NT), Benford's law, 11A41, 11N60, 11B99
Halász's theorem, uniformly distribution modulo 1, Mathematics - Number Theory, Weyl's criterion, Sequences and sets, Primes, Distribution functions associated with additive and positive multiplicative functions, divisor functions, multiplicative functions, Euler's function, FOS: Mathematics, Hecke eigenvalues of new forms, Number Theory (math.NT), Benford's law, 11A41, 11N60, 11B99
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