A bound of sums with convolutions of Dirichlet characters

Teerapat Srichan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 70–74
DOI: 10.7546/nntdm.2020.26.1.70-74
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Authors and affiliations

Teerapat Srichan
Department of Mathematics, Faculty of Science
Kasetsart University, Bangkok, Thailand

Abstract

We use the exponent pair to bound sums \sum_{ab\leq x}\chi_1(a)\chi_2(b), where \chi_1 and \chi_2 are primitive Dirichlet characters with conductors q_1 and q_2, respectively.

Keywords

  • Character sums
  • Dirichlet convolutions
  • Exponent pair

2010 Mathematics Subject Classification

  • Primary: 11L07
  • Secondary: 11N37, 11M06

References

  1. Banks, W. D., & Shparlinski, I. E. (2010). Sums with convolutions of Dirichlet characters, Manuscripta Math. 133, 105–144.
  2. Friedlander, J. B., & Iwaniec, H. (2005). Summation formulae for coefficients of
    L-functions, Canad. J. Math. 57, 494–505.
  3. Iwaniec, H., & Kowalski, E. (2004). Analytic Number Theory, American Mathematical Society, Providence.
  4. Richert, H. E. (1953). Über die Anzahl Abelscher Gruppen gegebener Ordnung. II., Math. Z., 58 (1), 71–84.

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Cite this paper

Srichan, T. (2020). A bound of sums with convolutions of Dirichlet characters. Notes on Number Theory and Discrete Mathematics, 26(1), 70-74, DOI: 10.7546/nntdm.2020.26.1.70-74.

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