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Mat. Zametki, 2016, Volume 100, Issue 2, Pages 185–195 (Mi mz10839)  

This article is cited in 2 scientific papers (total in 2 papers)

Intersections of Shifts of Multiplicative Subgroups

I. V. Vyuginab, E. V. Solodkovaa, I. D. Shkredovcda

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics" (HSE), Moscow
c P.G. Demidov Yaroslavl State University
d Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Using Stepanov's method, we obtain an upper bound for the cardinality of the intersection of additive shifts of several multiplicative subgroups of a finite field. The resulting inequality is applied to a question dealing with the additive decomposability of subgroups.

Keywords: multiplicative subgroup, finite field, Stepanov's method, sum of subgroups.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
Russian Foundation for Basic Research 14-01-00346
The work of the second and third authors (Secs. 1 and 3) was supported by the Russian Science Foundation under grant 14-11-00433. The work of the first author (Sec. 2) was supported by the Russian Foundation for Basic Research under grant 14-01-00346.


DOI: https://doi.org/10.4213/mzm10839

Full text: PDF file (508 kB)
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English version:
Mathematical Notes, 2016, 100:2, 189–198

Bibliographic databases:

Document Type: Article
UDC: 511.218
Received: 21.06.2015
Revised: 13.12.2015

Citation: I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “Intersections of Shifts of Multiplicative Subgroups”, Mat. Zametki, 100:2 (2016), 185–195; Math. Notes, 100:2 (2016), 189–198

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. D. Shkredov, “Differences of subgroups in subgroups”, Int. J. Number Theory, 14:4 (2018), 1111–1134  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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