Character sums estimates and an application to a problem of Balog

DOI10.1512/iumj.2022.71.8972OpenAlexW3014751857MaRDI QIDQ5093765

Tomasz Schoen, Ilya D. Shkredov

Publication date: 1 August 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.01885

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Estimates on character sums (11L40) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

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• On a question of Davenport and Lewis and new character sum bounds in finite fields
• On the number of incidences between points and planes in three dimensions
• Around Rédei's theorem
• On the Bogolyubov-Ruzsa lemma
• On the directions determined by a Cartesian product in an affine Galois plane
• Sums of multiplicative characters with additive convolutions
• New bounds in Balog-Szemerédi-Gowers theorem
• Another sum-product estimate in finite fields
• On additive decompositions of the set of quadratic residues modulo p
• Sums of Dilates
• Arithmetic problems in the theory of Dirichlet characters
• On asymptotic formulae in some sum–product questions
• Refined estimates concerning sumsets contained in the roots of unity
• Estimates for character sums with various convolutions

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