Published In
Transactions of the American Mathematical Society
Document Type
Article
Publication Date
12-1-2019
Subjects
Hecke operators -- Statistical aspects, Modular forms, Operator theory, Automorphic forms
Abstract
We prove a number of unconditional statistical results of the Hecke coefficients for unitary cuspidal representations of over number fields. Using partial bounds on the size of the Hecke coefficients, instances of Langlands functoriality, and properties of Rankin-Selberg -functions, we obtain bounds on the set of places where linear combinations of Hecke coefficients are negative. Under a mild functoriality assumption we extend these methods to . As an application, we obtain a result related to a question of Serre about the occurrence of large Hecke eigenvalues of Maass forms. Furthermore, in the cases where the Ramanujan conjecture is satisfied, we obtain distributional results of the Hecke coefficients at places varying in certain congruence or Galois classes.
Locate the Document
DOI
10.1090/tran/7903
Persistent Identifier
https://archives.pdx.edu/ds/psu/32713
Citation Details
CHIRIAC L, JORZA A. Comparing Hecke Coefficients of Automorphic Representations. Transactions of the American Mathematical Society. 2019;372(12):8871-8896. doi:10.1090/tran/7903.
Description
First published in Transactions of the American Mathematical Society in volume 372, 2019, published by the American Mathematical Society
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