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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2015_98_4_a9,
     author = {Yu. N. Shteinikov},
     title = {Estimates of {Trigonometric} {Sums} over {Subgroups} and {Some} of {Their} {Applications}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {606--625},
     publisher = {mathdoc},
     volume = {98},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a9/}
}
TY  - JOUR
AU  - Yu. N. Shteinikov
TI  - Estimates of Trigonometric Sums over Subgroups and Some of Their Applications
JO  - Matematičeskie zametki
PY  - 2015
SP  - 606
EP  - 625
VL  - 98
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a9/
LA  - ru
ID  - MZM_2015_98_4_a9
ER  - 
%0 Journal Article
%A Yu. N. Shteinikov
%T Estimates of Trigonometric Sums over Subgroups and Some of Their Applications
%J Matematičeskie zametki
%D 2015
%P 606-625
%V 98
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a9/
%G ru
%F MZM_2015_98_4_a9
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/