New estimates of double trigonometric sums with exponential functions

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dc.creatorGaraev, M. Z.
dc.creatorKaratsuba, A. A.
dc.date2005-04-01
dc.date.accessioned2026-07-07T05:18:44Z
dc.date.available2026-07-07T05:18:44Z
dc.descriptionWe establish a new bound for the exponential sum \begin{eqnarray*} \sum_{x\in\mathcal{X}}\Big|\sum_{y\in \mathcal{Y}}γ(y)\exp(2πi a λ^{xy}/p)\Big|, \end{eqnarray*} where $λ$ 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 $γ(n)$ are any complex numbers with $|γ(n)| \le 1.$ In particular, we improve several previously known bounds.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0504026
dc.identifierhttp://arxiv.org/abs/math/0504026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74766
dc.subjectNumber Theory
dc.subject11L07; 11L26; 11T23
dc.titleNew estimates of double trigonometric sums with exponential functions
dc.typetext

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