Sums of k-th powers and Fourier coefficients of cusp forms

In this paper, we will first establish a power saving result for the shifted convolution sums of k -th powers and the normalized Fourier coefficients of SL 2 ( Z ) cusp forms. Later we will generalize the result to higher rank cases.

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Bibliographic Details
Published inThe Ramanujan journal Vol. 60; no. 2; pp. 295 - 316
Main Author Wei, Zhining
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2023
Springer Nature B.V
Subjects
Combinatorics
Cusps
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Sums
Cusp forms
Shifted convolution sums
Circle method
11P55
11F30
Voronoi formula
11P05
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Summary:In this paper, we will first establish a power saving result for the shifted convolution sums of k -th powers and the normalized Fourier coefficients of SL 2 ( Z ) cusp forms. Later we will generalize the result to higher rank cases.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-022-00677-y