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J. Korean Math. Soc. 2024; 61(5): 899-922

Online first article August 26, 2024      Printed September 1, 2024

https://doi.org/10.4134/JKMS.j230096

Copyright © The Korean Mathematical Society.

Sign changes of the coefficients of triple product $L$-functions

Huixue Lao, Fengjiao Qiao

Shandong Normal University; Shandong Normal University

Abstract

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Let $f(z)$ be a primitive holomorphic cusp form and $g(z)$ be a Maass cusp form. In this paper, we give quantitative results for the sign changes of coefficients of triple product $L$-functions $L(f\times f\times f, s)$ and $L(f\times f\times g, s)$.

Keywords: Cusp forms, sign changes, two squares, triple product $L$-functions

MSC numbers: Primary 11F03, 11F11, 11F30

Supported by: This work was financially supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2018MA003).

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