English

The resonance method for large character sums

Number Theory 2014-01-14 v1

Abstract

We consider the size of large character sums, proving new lower bounds for the quantity Δ(N,q)=supχχ0modqn<Nχ(n)\Delta(N,q) = \sup_{\chi\neq \chi_0 mod q} |\sum_{n < N} \chi(n)| for almost all ranges of NN. The results are proven using the resonance method and saddle point analysis.

Keywords

Cite

@article{arxiv.1109.1786,
  title  = {The resonance method for large character sums},
  author = {Bob Hough},
  journal= {arXiv preprint arXiv:1109.1786},
  year   = {2014}
}
R2 v1 2026-06-21T19:01:56.229Z