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 Trudy Mat. Inst. Steklova, 2018, Volume 303, Pages 45–58 (Mi tm3941)

Estimates for character sums in finite fields of order $p^2$ and $p^3$

M. R. Gabdullinab

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
b N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia

Abstract: We obtain nontrivial bounds on character sums over “boxes” of volume $p^{n(1/4+\varepsilon)}$ in finite fields of order $p^n$ for $n=2$ and $n=3$.

 Funding Agency Grant Number Russian Science Foundation 14-11-00702 This work is supported by the Russian Science Foundation under grant 14-11-00702.

DOI: https://doi.org/10.1134/S0371968518040052

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 303, 36–49

Bibliographic databases:

UDC: 511.33

Citation: M. R. Gabdullin, “Estimates for character sums in finite fields of order $p^2$ and $p^3$”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 45–58; Proc. Steklov Inst. Math., 303 (2018), 36–49

Citation in format AMSBIB
\Bibitem{Gab18} \by M.~R.~Gabdullin \paper Estimates for character sums in finite fields of order $p^2$ and $p^3$ \inbook Harmonic analysis, approximation theory, and number theory \bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday \serial Trudy Mat. Inst. Steklova \yr 2018 \vol 303 \pages 45--58 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3941} \crossref{https://doi.org/10.1134/S0371968518040052} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3723996} \elib{https://elibrary.ru/item.asp?id=37045251} \transl \jour Proc. Steklov Inst. Math. \yr 2018 \vol 303 \pages 36--49 \crossref{https://doi.org/10.1134/S0081543818080059} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000460475900005} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062492965}