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Matematicheskie Zametki, 1969, Volume 5, Issue 3, Pages 373–380
(Mi mzm6857)
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This article is cited in 2 scientific papers (total in 2 papers)
Estimation of a sum along an algebraic curve
G. I. Perel'muter Saratov State University named after N. G. Chernyshevsky
Abstract:
Let $\Gamma$ be an algebraic curve determined over a finite field $k=[q]$; $e$, $\chi$ are subsidiary additive and multiplicative characters of the field $k$; $\varphi$, $\psi$ are functions in $\Gamma$ determined over $k$ and satisfying some natural conditions. If $P$ passes through the points of curve $\Gamma$, rational over $k$, then
$$
\biggl|\sum_{P\in\Gamma}e(\varphi(P))\chi(\psi(P))\biggr|\leqslant C\sqrt q
$$
where constant $C$ depends only on the powers of $\Gamma,\varphi,\psi$.
Received: 17.05.1968
Citation:
G. I. Perel'muter, “Estimation of a sum along an algebraic curve”, Mat. Zametki, 5:3 (1969), 373–380; Math. Notes, 5:3 (1969), 223–227
Linking options:
https://www.mathnet.ru/eng/mzm6857 https://www.mathnet.ru/eng/mzm/v5/i3/p373
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