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Published October 2021 | Accepted Version
Journal Article Open

Average of Dirichlet coefficients of cuspidal representations related to GL(2)

Abstract

Let π be a cuspidal representation on GL(2,A_Q) We give nontrivial lower and upper bounds for average of absolute values of Dirichlet coefficients associated to π; and nontrivial upper bound in the case of Sym^kπ, k= 2,3. These bounds generalize the known estimates in holomorphic case to Maass forms, without assuming the Ramanujan–Petersson conjecture.

Additional Information

© 2021 Springer Science+Business Media, LLC, part of Springer Nature. Received 05 December 2019. Accepted 02 November 2020. Published 18 February 2021. I am very grateful to Nahid Walji for his helpful comments. I would like to thank Yujiao Jiang, Philippe Michel, Zhi Qi, Maksym Radziwill and Dinakar Ramakrishnan for their precise comments and valuable suggestions. Sincere thanks are also due to Bingyi Chen for his help on numerical analysis. I am also immensely grateful to the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.

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Additional details

Created:
August 22, 2023
Modified:
October 23, 2023