Bounds for moments of quadratic Dirichlet character sums of prime moduli

2024/12/26 by Yuetong Zhao, Zhao, Yuetong
Mathematics · #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.19151

Abstract

Assuming the generalized Riemann hypothesis, we evaluate sharp upper bounds for the shifted moments of quadratic Dirichlet L-functions with moduli 8p, where p ranges over odd primes. We then apply this result to prove bounds for the moments of quadratic Dirichlet character sums with prime moduli.

Citations

• On character sums and class numbers

Related

• Shifted moments of quadratic Dirichlet L-functions
• Moments of quadratic Dirichlet character sums
• Shifted moments of cubic and quartic Dirichlet L-functions
• Upper bounds for shifted moments of Dirichlet L-functions to a fixed modulus over function fields
• A lower bound on high moments of character sums