On Benford’s law for multiplicative functions
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- by Vorrapan Chandee, Xiannan Li, Paul Pollack and Akash Singha Roy
- Proc. Amer. Math. Soc. 151 (2023), 4607-4619
- DOI: https://doi.org/10.1090/proc/16480
- Published electronically: July 14, 2023
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Abstract:
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.References
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Bibliographic Information
- Vorrapan Chandee
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66503
- MR Author ID: 880105
- Email: chandee@ksu.edu
- Xiannan Li
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66503
- MR Author ID: 867056
- Email: xiannan@math.ksu.edu
- Paul Pollack
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 830585
- Email: pollack@uga.edu
- Akash Singha Roy
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 1449066
- Email: akash01s.roy@gmail.com
- Received by editor(s): April 1, 2022
- Received by editor(s) in revised form: April 12, 2022, August 22, 2022, November 29, 2022, December 7, 2022, and March 12, 2023
- Published electronically: July 14, 2023
- Additional Notes: The first author was supported by the Simons Foundation Collaboration Grant for Mathematicians and NSF grant DMS-2101806
The second author was supported by the Simons Foundation Collaboration Grant for Mathematicians
The third author was supported by NSF grant DMS-2001581 - Communicated by: Amanda Folsom
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4607-4619
- MSC (2020): Primary 11N60, 11A41, 11B99
- DOI: https://doi.org/10.1090/proc/16480
- MathSciNet review: 4634867