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Mat. Zametki, 1973, Volume 14, Issue 1, Pages 73–81 (Mi mz7206)  

This article is cited in 2 scientific papers (total in 2 papers)

Estimate of a sum of Legendre symbols of polynomials of even degree

D. A. Mit'kin

M. V. Lomonosov Moscow State University

Abstract: Let $n\ge4$ be even, $p>\frac{n^2-2n}2$ be simple odd, and $f(x)=a_0+a_1x+…+a_nx^n$ be a polynomial with integral coefficients that are not quadratic over the residue field modulo $p$, $(a_n,p)=1$. The following inequality is proved:
$$ |\sum_{x=1}^p(\frac{f(x)}p)|\le(n-2)\sqrt{p+1-\frac{n(n-4)}4}+1. $$


Full text: PDF file (418 kB)

English version:
Mathematical Notes, 1973, 14:1, 597–602

Bibliographic databases:

Document Type: Article
UDC: 511.3
Received: 07.07.1972

Citation: D. A. Mit'kin, “Estimate of a sum of Legendre symbols of polynomials of even degree”, Mat. Zametki, 14:1 (1973), 73–81; Math. Notes, 14:1 (1973), 597–602

Citation in format AMSBIB
\Bibitem{Mit73}
\by D.~A.~Mit'kin
\paper Estimate of a~sum of Legendre symbols of polynomials of even degree
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 1
\pages 73--81
\mathnet{http://mi.mathnet.ru/mz7206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=332794}
\zmath{https://zbmath.org/?q=an:0281.10016}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 1
\pages 597--602
\crossref{https://doi.org/10.1007/BF01095777}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. E. Shparlinski, “On some problems in the theory of finite fields”, Russian Math. Surveys, 46:1 (1991), 199–240  mathnet  crossref  mathscinet  zmath  adsnasa
    2. Andrica D. Crisan V., “On Some Special Legendre Sums of the Form SIGMA(P-1)(X=1) (F(X)/P) G(X)”, Analele Stiint. Univ. Ovidius C., 25:3 (2017), 37–44  crossref  isi
  • Математические заметки Mathematical Notes
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