
TL;DR
This paper establishes a new lower bound for large character sums over specific ranges, improving previous results and aligning with expected maximal values as the range parameter diminishes.
Contribution
It provides a novel lower bound for large character sums in a wide range, extending prior work by Granville and Soundararajan.
Findings
New lower bound for character sums when x = q / (log q)^B
Improved understanding of maximal character sums for large ranges
Results recover expected maximal values as B approaches zero
Abstract
In this paper, we prove a lower bound for , when . This improves on a result of Granville and Soundararajan for large character sums when the range of summation is wide. When goes to zero, our lower bound recovers the expected maximal value of character sums for most characters.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Analytic Number Theory Research · Finite Group Theory Research
