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Matematicheskie Zametki, 1969, Volume 5, Issue 3, Pages 373–380 (Mi mzm6857)  

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
Full-text PDF (636 kB) Citations (2)
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
English version:
Mathematical Notes, 1969, Volume 5, Issue 3, Pages 223–227
DOI: https://doi.org/10.1007/BF01388632
Bibliographic databases:
UDC: 513.6
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Per69}
\by G.~I.~Perel'muter
\paper Estimation of a~sum along an~algebraic curve
\jour Mat. Zametki
\yr 1969
\vol 5
\issue 3
\pages 373--380
\mathnet{http://mi.mathnet.ru/mzm6857}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=241424}
\zmath{https://zbmath.org/?q=an:0188.53302|0179.49903}
\transl
\jour Math. Notes
\yr 1969
\vol 5
\issue 3
\pages 223--227
\crossref{https://doi.org/10.1007/BF01388632}
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  • https://www.mathnet.ru/eng/mzm/v5/i3/p373
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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