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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
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.
Received: 02.07.2018
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
Linking options:
https://www.mathnet.ru/eng/mzm12124https://doi.org/10.4213/mzm12124 https://www.mathnet.ru/eng/mzm/v106/i2/p212
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Abstract page: | 305 | Full-text PDF : | 34 | References: | 36 | First page: | 12 |
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