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The average behaviour of Hecke eigenvalues over certain sparse sequence of positive integers.
- Source :
-
Research in Number Theory . 10/22/2022, Vol. 8 Issue 4, p1-20. 20p. - Publication Year :
- 2022
-
Abstract
- Let j ≥ 2 be a given integer. Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = S L (2 , Z) . Denote by λ sym j f (n) the nth normalized coefficient of the Dirichlet expansion of the jth symmetric power L-function L (sym j f , s) attached to f. In this paper, we are interested in the average behaviour of the following sum ∑ a 2 + b 2 + c 2 + d 2 ≤ x (a , b , c , d) ∈ Z 4 λ sym j f 2 (a 2 + b 2 + c 2 + d 2) , where x is sufficiently large, which improves and generalizes the recent work of Sharma and Sankaranarayanan [52]. By analogy, we also consider the analogous results for higher moments of normalized Fourier coefficients and the second moment of normalized coefficients of two symmetric power L-functions attached to two distinct cusp forms of the same sequence. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CUSP forms (Mathematics)
*MODULAR groups
*EIGENVALUES
*L-functions
Subjects
Details
- Language :
- English
- ISSN :
- 25220160
- Volume :
- 8
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Research in Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 159839326
- Full Text :
- https://doi.org/10.1007/s40993-022-00403-z