Resonance between the Representation Function and Exponential Functions over Arithemetic Progression

Li Ma, Xiaofei Yan and Tianping Zhang

Journal of Mathematics, 2021, vol. 2021, 1-10

Abstract: Let rn denote the number of representations of a positive integer n as a sum of two squares, i.e., n=x12+x22, where x1 and x2 are integers. We study the behavior of the exponential sum twisted by rn over the arithmetic progressions ∑n∼Xn≡lmodqrneαnβ, where 0≠α∈℠, 0 1 is a large parameter, 1≤l≤q are integers, and l,q=1. We obtain the upper bounds in different situations.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6616348

DOI: 10.1155/2021/6616348

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