Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Vyugin, Ilya"'
Autor:
Aleshina, Sofia, Vyugin, Ilya
We generalize two results about subgroups of multiplicative group of finite field of prime order. In particular, the lower bound on the cardinality of the set of values of polynomial $P(x,y)$ is obtained under the certain conditions, if variables $x$
Externí odkaz:
http://arxiv.org/abs/2008.08684
We obtain a new bound for the number of solutions to polynomial equations in cosets of multiplicative subgroups in finite fields, which generalises previous results of P. Corvaja and U. Zannier (2013). We also obtain a conditional improvement of rece
Externí odkaz:
http://arxiv.org/abs/2005.05315
Autor:
Vyugin, Ilya
Let $f_1(x),\ldots,f_n(x)$ be some polynomials. The upper bound on the number of $x\in\mathbb F_p$ such that $f_1(x),\ldots,f_n(x)$ are roots of unit of order $t$ is obtained. This bound generalize the bound of the paper \cite{V-S} to the case of pol
Externí odkaz:
http://arxiv.org/abs/1811.08930
Autor:
Vyugin, Ilya, Levin, Roman
In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.
Externí odkaz:
http://arxiv.org/abs/1702.08323
Autor:
Vyugin, Ilya, Makarychev, Sergey
We present a new proof of Corvaja and Zannier's \cite{C-Z} the upper bound of the number of solutions $(x,y)$ of the algebraic equation $P(x,y)=0$ over a field $\mathbb{F}_p$ ($p$ is a prime), in the case, where $x\in g_1G$, $y\in g_2G$, ($g_1G$, $g_
Externí odkaz:
http://arxiv.org/abs/1504.01354
Autor:
Gontsov, Renat, Vyugin, Ilya
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular ones and pr
Externí odkaz:
http://arxiv.org/abs/1312.2518
The paper is devoted to some applications of Stepanov method. In the first part of the paper we obtain the estimate of the cardinality of the set, which is obtained as an intersection of additive shifts of some different subgroups of F^*_p. In the se
Externí odkaz:
http://arxiv.org/abs/1302.3839
Autor:
Vyugin, Ilya
A local behavior of solutions of the Schlesinger equation is studied. We obtain expansions for this solutions, which converge in some neighborhood of a singular point. As a corollary the similar result for the sixth Painlev\'e equation was obtained.
Externí odkaz:
http://arxiv.org/abs/1212.2176
Akademický článek
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Autor:
Makarychev, Sergei, Vyugin, Ilya
Publikováno v:
Arnold Mathematical Journal; Mar2019, Vol. 5 Issue 1, p105-121, 17p