Large character sums: Burgess's theorem and zeros of \(L\)-functions

DOI10.4171/JEMS/757zbMath1444.11177arXiv1501.01804OpenAlexW2964106378MaRDI QIDQ679660

Andrew Granville, Kannan Soundararajan

Publication date: 19 January 2018

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.01804

zbMATH Keywords

multiplicative functionsbounds on character sumszeros of Dirichlet \(L\)-functions

Mathematics Subject Classification ID

Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Estimates on character sums (11L40) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (9)

Gaussian phenomena for small quadratic residues and non-residues ⋮ One-level density estimates for Dirichlet \(L\)-functions with extended support ⋮ Multiplicative functions in short arithmetic progressions ⋮ On character sums with determinants ⋮ The distribution of values of zeta and \(L\)-functions ⋮ Large sums of high‐order characters ⋮ Quadratic nonresidues below the Burgess bound ⋮ Weak subconvexity without a Ramanujan hypothesis ⋮ An unconditional improvement to the running time of the quadratic Frobenius test

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• Decay of Mean Values of Multiplicative Functions
• Density of non-residues in Burgess-type intervals and applications
• On Character Sums and L -Series. II
• The spectrum of multiplicative functions

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