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Summation formulae of multiplicative functions over arithmetic progressions and applications

Part of: Multiplicative number theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  12 April 2024

Yujiao Jiang  and
Guangshi Lü
Yujiao Jiang*
Affiliation:
School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China
Guangshi Lü
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

In this paper, we investigate the asymptotic distribution of a class of multiplicative functions over arithmetic progressions without the Ramanujan conjecture. We also apply these results to some interesting arithmetic functions in automorphic context, such as coefficients of automorphic L-functions, coefficients of their Rankin–Selberg.

Keywords

Multiplicative functionsarithmetic progressionsautomorphic L-functions

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions 11F30: Fourier coefficients of automorphic forms
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFA1000700), the National Natural Science Foundation of China (Grant Nos. 12271297 and 12031008), and the Natural Science Foundation of Shandong Province (Grant No. ZR2022YQ03).

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