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Matematicheskie Zametki, 1976, Volume 20, Issue 6, Pages 815–824 (Mi mzm7910)  
Estimate of a multidimensional sum with the Legendre symbol for a polynomial of odd degree

G. I. Perel'muter

Saratov State University
Full-text PDF (713 kB)
Abstract: The estimate
$$ \Bigl|\sum_{x,1\dots,x_n\in F_q}\chi(f(x_1,\dots,x_n))\Bigr|\le(d-1)^nq^{n/2}. $$
is derived for the quadratic character Lambda of a field $F_q$ of $q$ elements and a polynomial $f$ of odd degree $d$ over $F_q$ under certain natural conditions.
Received: 21.03.1975
English version:
Mathematical Notes, 1976, Volume 20, Issue 6, Pages 1015–1020
DOI: https://doi.org/10.1007/BF01095194
Bibliographic databases:
UDC: 513.6
Language: Russian
Citation: G. I. Perel'muter, “Estimate of a multidimensional sum with the Legendre symbol for a polynomial of odd degree”, Mat. Zametki, 20:6 (1976), 815–824; Math. Notes, 20:6 (1976), 1015–1020
Citation in format AMSBIB
\Bibitem{Per76}
\by G.~I.~Perel'muter
\paper Estimate of a~multidimensional sum with the Legendre symbol for a~polynomial of odd degree
\jour Mat. Zametki
\yr 1976
\vol 20
\issue 6
\pages 815--824
\mathnet{http://mi.mathnet.ru/mzm7910}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=444669}
\zmath{https://zbmath.org/?q=an:0381.12011}
\transl
\jour Math. Notes
\yr 1976
\vol 20
\issue 6
\pages 1015--1020
\crossref{https://doi.org/10.1007/BF01095194}
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    		Математические заметки Mathematical Notes
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