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А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 22, 2017 10:45, Moscow, Steklov Mathematical Institute
 


Applications of incidences theory to some triple exponential sums

I. D. Shkredovab

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 253.3 Mb

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I. D. Shkredov
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Abstract: Let $\chi$ be a nonprincipal multiplicative character modulo a prime number $p$. Using the incidences theory over $\mathbf{F}_p\times \mathbf{F}_p \times \mathbf{F}_p$, we find new bounds for the sums
\begin{multline*} \sum\limits_{a\in A, b\in B, c\in C} \chi(a+b+c), \sum\limits_{a\in A, b\in B, c\in C, d\in D} \chi (a+b+cd),\quad \sum\limits_{a\in A, b\in B, c\in C, d\in D} \chi (a+b(c+d)) \end{multline*}
over arbitrary sets, and for a trinomial sum
$$ \sum_x \chi(x) e_p (ax^k +bx^m + cx^n)  . $$


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