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Мemorial conference dedicated to the memory of Ivan Matveevich Vinogradov
March 28, 2019 15:30–15:55, Moscow, Steklov Mathematical Institute, Conference hall
 


Incomplete Kloosterman sums and solvability of some congruences with prime variables

M. A. Korolevab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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MP4 475.1 Mb

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M. A. Korolev
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Abstract: The talk is devoted to a new estimate for a special incomplete Kloosterman sum and its applications to the problems of the solvability of some congruences modulo $q$. The variables in these congruences run through prime numbers lying in the short interval of the type $(1,N]$, where $N\ll q^{1-c}$, $c>0$.

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