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28 March 2024
 
  » arxiv » math.NT/0504026

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New estimates of double trigonometric sums with exponential functions
M. Z. Garaev ; A. A. Karatsuba ;
Date 1 Apr 2005
Subject Number Theory MSC-class: 11L07; 11L26; 11T23 | math.NT
AbstractWe establish a new bound for the exponential sum egin{eqnarray*} sum_{xinmathcal{X}}Big|sum_{yin mathcal{Y}}gamma(y)exp(2pi i a lambda^{xy}/p)Big|, end{eqnarray*} where $lambda$ is an element of the residue ring modulo a large prime number $p,$ $mathcal{X}$ and $mathcal{Y}$ are arbitrary subsets of the residue ring modulo $p-1$ and $gamma(n)$ are any complex numbers with $|gamma(n)| le 1.$ In particular, we improve several previously known bounds.
Source arXiv, math.NT/0504026
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