Coefficients of symmetric power L-functions on integers under digital constraints

Khadija Mbarki
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 4, Pages 875–883
DOI: 10.7546/nntdm.2025.31.4.875-883
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Authors and affiliations

Khadija Mbarki
Faculté des sciences de Monastir, Département de Mathématiques
Monastir 5000, Tunisie

Abstract

Let \lambda_{{\rm sym}^{r}f}(n) be the n-th coefficient in the Dirichlet series representing the symmetric power L-function attached to a primitive form f of weight k and level N. In this paper, we give asymptotic formulas for the arithmetic mean of \lambda_{{\rm sym}^{r}f}(n) on integers under digital constraints related to the sum of digits function. Our results throw the light on the behavior of the classical function \lambda_{{\rm sym}^{r}f}(n) on integers in arithmetic progression related to the sum of digits function.

Keywords

  • Modular forms
  • L-functions
  • Dirichlet coefficients
  • Sum of digits function
  • Arithmetic progression

2020 Mathematics Subject Classification

  • 11N37
  • 11T23

References

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Manuscript history

  • Received: 12 June 2025
  • Revised: 12 November 2025
  • Accepted: 15 November 2025
  • Online First: 4 December 2025

Copyright information

Ⓒ 2025 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Mbarki, K. (2025). Coefficients of symmetric power L-functions on integers under digital constraints. Notes on Number Theory and Discrete Mathematics, 31(4), 875-883, DOI: 10.7546/nntdm.2025.31.4.875-883.

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