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Conference in memory of A. A. Karatsuba on number theory and applications
January 31, 2014 17:35, Moscow, Steklov Mathematical Institute, Lecture Room 530
 


On the Heilbronn's exponential sum

I. D. Shkredov
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I. D. Shkredov


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Abstract: The number $(q^{n-1}-1)/p$ from $\mathbb{Z}/p\mathbb{Z}$ is called as Fermat quotient (here $p$ is prime and $n$ is nonzero integer). The problems of distribution of Fermat quotients are connected with the upper bounds for so-called Heilbronn's exponential sum.
The first non-trivial bound for such sum was obtained by Heath-Brown and then improved by Heath -Brown and Konyagin. The talk is devoted to the recent improvements of Heath-Brown and Konyagin's result.

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