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

Liyang Yang

doi:10.1007/s11139-020-00360-0

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

Liyang Yang

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let π be a cuspidal representation on GL(2,AQ). 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.

Original language	English (US)
Pages (from-to)	203-234
Number of pages	32
Journal	Ramanujan Journal
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/s11139-020-00360-0
State	Published - Oct 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

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

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10.1007/s11139-020-00360-0

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abstract = "Let π be a cuspidal representation on GL(2,AQ). 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.",

keywords = "Hecke eigenvalues, Ramanujan–Petersson conjecture, Symmetric power representations of GL(2)",

author = "Liyang Yang",

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T1 - Average of Dirichlet coefficients of cuspidal representations related to GL(2)

AU - Yang, Liyang

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N2 - Let π be a cuspidal representation on GL(2,AQ). 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.

AB - Let π be a cuspidal representation on GL(2,AQ). 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.

KW - Hecke eigenvalues

KW - Ramanujan–Petersson conjecture

KW - Symmetric power representations of GL(2)

UR - https://www.scopus.com/pages/publications/85101252386

UR - https://www.scopus.com/pages/publications/85101252386#tab=citedBy

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DO - 10.1007/s11139-020-00360-0

M3 - Article

AN - SCOPUS:85101252386

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JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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