Geodesic
Estimates of Trigonometric Sums over Subgroups and Some of Their Applications
Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 606-625.

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In this paper, we obtain new upper bounds for trigonometric sums over subgroups $\Gamma \subset \mathbb Z_{p}^{*}$ whose size belongs to $[p^{28/95},p^{182/487}]$. Using an approach due to Malykhin, we refine estimates of such sums in $\mathbb Z_{p^{r}}^{*}$ and apply them to the divisibility problem for Fermat quotients.
Keywords: trigonometric sum over a subgroup, coset with respect to a subgroup, set with small multiplicative doubling, Plunnecke's inequality.
Mots-clés : Fermat quotient, Abel transformation 
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Yu. N. Shteinikov. Estimates of Trigonometric Sums over Subgroups and Some of Their Applications. Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 606-625. http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a9/

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