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

Yang, Liyang (2021) Average of Dirichlet coefficients of cuspidal representations related to GL(2). Ramanujan Journal . ISSN 1382-4090. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20210222-100903917

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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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/s11139-020-00360-0	DOI	Article
https://rdcu.be/cfHSC	Publisher	Free ReadCube access
https://arxiv.org/abs/1911.02148	arXiv	Discussion Paper

ORCID:

Author	ORCID
Yang, Liyang	0000-0001-6988-2927

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.

Subject Keywords:

Hecke eigenvalues; Symmetric power representations of GL(2); Ramanujan–Petersson conjecture

Classification Code:

Mathematics Subject Classification: 11F66; 11F70

Record Number:

CaltechAUTHORS:20210222-100903917

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20210222-100903917

Official Citation:

Yang, L. Average of Dirichlet coefficients of cuspidal representations related to GL(2). Ramanujan J (2021). https://doi.org/10.1007/s11139-020-00360-0

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No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

108141

Collection:

CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

23 Feb 2021 18:01

Last Modified:

23 Feb 2021 18:01

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