The mean square of real character sums
Peng Gao

TL;DR
This paper evaluates a smoothed sum involving the Kronecker symbol over positive odd square-free integers, providing insights into the mean square of real character sums in number theory.
Contribution
It introduces a new evaluation of a specific smoothed sum of real character sums involving the Kronecker symbol over square-free integers.
Findings
Derived an explicit asymptotic formula for the sum
Established bounds for the mean square of real character sums
Enhanced understanding of character sum behavior in number theory
Abstract
In this paper, we evaluate a smoothed sum of the form , where is the Kronecker symbol and denotes a sum over positive odd square-free integers.
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Taxonomy
TopicsAnalytic Number Theory Research · Limits and Structures in Graph Theory · Coding theory and cryptography
