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Matematicheskie Zametki, 2010, Volume 88, Issue 6, Pages 859–866
DOI: https://doi.org/10.4213/mzm8562 (Mi mzm8562) 		 
This article is cited in 3 scientific papers (total in 3 papers)

An Estimate for the Sum of Legendre Symbols

E. A. Grechnikov

M. V. Lomonosov Moscow State University
Full-text PDF (418 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm8562
Abstract: For the sum S of the Legendre symbols of a polynomial of odd degree n⩾3 modulo primes p⩾3, Weil's estimate |S|⩽(n−1)√p and Korobov's estimate
|S|⩽(n−1)√p−(n−3)(n−4)4forp⩾n2+92
are well known. In this paper, we prove a stronger estimate, namely,
|S|<(n−1)√p−(n−3)(n+1)4.
Keywords: polynomial of odd degree, Legendre symbol, Weil's estimate, Korobov's estimate.
Received: 15.07.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 6, Pages 819–826
DOI: https://doi.org/10.1134/S0001434610110222
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. A. Grechnikov, “An Estimate for the Sum of Legendre Symbols”, Mat. Zametki, 88:6 (2010), 859–866; Math. Notes, 88:6 (2010), 819–826
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    1. Guo W., Liu X., Zhang T., “Dirichlet Characters of the Rational Polynomials”, AIMS Math., 7:3 (2021), 3494–3508  crossref  mathscinet  isi  scopus
    2. Pandey R.K., Parashar A., “On Certain Sums With Quadratic Expressions Involving the Legendre Symbol”, J. Integer Seq., 21:4 (2018), 18.4.7  mathscinet  zmath  isi
    3. 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  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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