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Matematicheskie Zametki, 2015, Volume 98, Issue 4, Pages 606–625
DOI: https://doi.org/10.4213/mzm10629 (Mi mzm10629) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Estimates of Trigonometric Sums over Subgroups and Some of Their Applications

Yu. N. Shteinikov

Steklov Mathematical Institute of Russian Academy of Sciences
Full-text PDF (587 kB) Citations (14)
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DOI: https://doi.org/10.4213/mzm10629
Abstract: 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, Fermat quotient, coset with respect to a subgroup, set with small multiplicative doubling, Abel transformation, Plunnecke's inequality.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant 14-11-00433.
Received: 18.11.2014
Revised: 18.03.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 4, Pages 667–684
DOI: https://doi.org/10.1134/S0001434615090333
Bibliographic databases:
Document Type: Article
UDC: 511.321
Language: Russian
Citation: Yu. N. Shteinikov, “Estimates of Trigonometric Sums over Subgroups and Some of Their Applications”, Mat. Zametki, 98:4 (2015), 606–625; Math. Notes, 98:4 (2015), 667–684
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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