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International conference ''Algebra, algebraic geometry and number theory'' dedicated to the memory of academician Igor Rostislavovich Shafarevich
June 14, 2018 14:30–15:30, Moscow, Steklov Mathematical Institute of RAS, 8, Gubkina str., Conference hall
 


Large values of short character sums

A. B. Kalmynin

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A. B. Kalmynin

Abstract: It is well-known that sums of values of non-principal Dirichlet characters over large enough intervals can be estimated non-trivially. However, it turns out that for any $A>0$ there exist infinitely many primes $p$ for which there is no non-trivial bound for the sum of values of quadratic character modulo $p$ over the interval of length $(\log p)^A$. We will discuss the proof of this result and its possible generalizations.

Language: English

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