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On the sign changes of Dirichlet coefficients of triple product L-functions

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  14 November 2024

Jinzhi Feng
Jinzhi Feng*
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China
*
e-mail: fengjinzhi@mail.sdu.edu.cn
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Abstract

Let f and g be two distinct normalized primitive holomorphic cusp forms of even integral weight $k_{1}$ and $k_{2}$ for the full modular group $SL(2,\mathbb {Z})$, respectively. Suppose that $\lambda _{f\times f\times f}(n)$ and $\lambda _{g\times g\times g}(n)$ are the n-th Dirichlet coefficient of the triple product L-functions $L(s,f\times f\times f)$ and $L(s,g\times g\times g)$. In this paper, we consider the sign changes of the sequence $\{\lambda _{f\times f\times f}(n)\}_{n\geq 1}$ and $\{\lambda _{f\times f\times f}(n)\lambda _{g\times g\times g}(n)\}_{n\geq 1}$ in short intervals and establish quantitative results for the number of sign changes for $n \leq x$, which improve the previous results.

Keywords

sign changeDirichlet coefficientcusp form

MSC classification

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F30: Fourier coefficients of automorphic forms 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 4 , December 2024 , pp. 1092 - 1106
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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