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Matematicheskie Zametki, 2019, Volume 106, Issue 2, Pages 212–221
DOI: https://doi.org/10.4213/mzm12124 (Mi mzm12124) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A Bound for the Number of Preimages of a Polynomial Mapping

I. V. Vyuginabc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University "Higher School of Economics", Moscow
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/mzm12124
Abstract: An upper bound for the number of field elements that can be taken to roots of unity of fixed multiplicity by means of several given polynomials is obtained. This bound generalizes the bound obtained by V'yugin and Shkredov in 2012 to the case of polynomials of degree higher than $1$. This bound was obtained both over the residue field modulo a prime and over the complex field.
Keywords: polynomial, field, subgroup, Stepanov's method.
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: 02.07.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 2, Pages 203–211
DOI: https://doi.org/10.1134/S0001434619070241
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: I. V. Vyugin, “A Bound for the Number of Preimages of a Polynomial Mapping”, Mat. Zametki, 106:2 (2019), 212–221; Math. Notes, 106:2 (2019), 203–211
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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