M. R. Gabdullin, “Estimates for character sums in finite fields of order <nobr>$p^2$</nobr> and <nobr>$p^3$</nobr>”, Trudy Mat. Inst. Steklova, 2018, Volume 303,Pages <nobr>45–58</nobr>

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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

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. Gabdullin^ab

^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 $n=3$.

UDC: 511.33

Received: April 1, 2018

DOI: 10.1134/S0371968518040052

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

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