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Some applications of representation theory to the sum-product phenomenon

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arxiv 2307.03156 v1 pith:NUDD7APL submitted 2023-07-06 math.NT math.COmath.GR

Ilya D. Shkredov This is my paper · ORCID
classification math.NTmath.COmath.GR
keywords theoryapplicationsrepresentationcharactersconjectureestimatingincidencesintroduce
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In our paper, we introduce a new method for estimating incidences via representation theory. We obtain several applications to various sums with multiplicative characters and to Zaremba's conjecture from number theory.

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  1. On some results of Korobov and Larcher and Zaremba's conjecture

    math.NT 2026-03 accept novelty 7.0 of 10

    Zaremba's conjecture holds for all large primes: an absolute M exists so every large prime p admits a coprime a whose continued-fraction partial quotients are all ≤ M, with quantitative lower bounds on the number of such a.

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