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Пересечения сдвигов мультипликативных подгрупп
Математические заметки. 2016. Т. 100. № 2. С. 185-195.
By means Stepanov's method the bound of cardinality of the intersection of additive shifts of several subgroups of multiplicative group of the finite field was obtained. This bound apply to some question of additive decomposition of subgroups.
Макарычев С. В., Vyugin I. V., Arnold Mathematical Journal 2019 Vol. 5 No. 1 P. 105-121
We present an upper bound on the number of solutions of an algebraic equation P(x,y)=0 where x and y belong to the union of cosets of some subgroup of the multiplicative group κ∗ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also ...
Added: August 13, 2019
Vyugin I. V., Математические заметки 2019 Т. 106 № 2 С. 212-221
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 ...
Added: October 9, 2019
Vyugin I. V., Макарычев С. В., Shparlinski I. et al., Quarterly Journal of Mathematics 2020 Vol. 71 No. 2 P. 637-648
We sharpen the bounds of J. Bourgain, A. Gamburd and P. Sarnak (2016) on the possible number of nodes outside the ‘giant component’ and on the size of individual connected components in the suitably defined functional graph of Markoff triples modulo p. This is a step towards the conjecture that there are no such nodes at ...
Added: September 12, 2020
Vyugin I. V., Макарычев С. В., Arnold Mathematical Journal 2019
In this paper we present a new bound of the number of solutions of a polynomial equation $P(x,y)=0$ over the field $\overline{\mathbb{F}}_p$ that belong to a union of cosets $(x,y)\in\bigcup_{i=1}^hg_i'G\times g_i''G$.
This bound improves a case of the bound of Corvaja and Zannier (see \cite{C-Z}) in the case $h\gg 1$. Using this bound we obtain estimates ...
Added: December 14, 2017
Гриценко В. В., Maevsky A. E., Математические заметки 2014 Т. 96 № 5-6 С. 864-879
В статье изучается алгебра p(x)-циркулянтов над произвольным конечным полем и строятся алгоритмы случайного равновероятного выбора элементов из подмножества всех обратимых p(x)-циркулянтов или подмножества всех p(x)-циркулянтов с заданным значением определителя. Особенностью рассматриваемых алгоритмов является минимизация временной сложности и количества случайных элементов, используемых в процессе их работы. ...
Added: October 21, 2015
Vyugin I. V., Макарычев С. В., / Cornell University. Series arXiv "math". 2015.
We present an upeer bound of the number of solutions (x,y) of a polynomial equation P(x,y)=0 over a field F_p in the case where x,y from G, G is a subgroup of F_p^*. ...
Added: June 22, 2015
Vyugin I. V., Shkredov I. D., Solodkova E. V., / Cornell University. Series math "arxiv.org". 2014.
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 second part we prove a new upper bound for Heilbron's exponential ...
Added: September 2, 2014
Popov V., / Centro Internazionale per la Ricerca Matematica. Series CIRM "Electronic preprint server". 2012. No. нет.
Some problems on the structure of the Cremona groups formulated (with comments) by the author at the International conference Birational and Affine Geometry, Levico Terme (Trento), 29.10.12--03.11.12 ...
Added: January 9, 2013
В. Л. Попов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2016 Т. 468 № 5 С. 499-501
A general theorem on the purity of of invariant field extensions
is proved. Using it, a criterion of rational triangulability of connected solvable
affine algebraic subgroups of the Cremona groups is obtained. This criterion is
applied for proving the existence of rationally nontriangulable subgroups of the
above form and for proving their stable rational triangulability. The latter property
answers in ...
Added: May 16, 2016
Galkin S., Rybakov S., Mathematical notes 2019 Vol. 106 No. 6 P. 1014-1018
For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good tower over k=F_{p^2}, that is optimal if p=3. ...
Added: January 29, 2020
Loughran D., Trepalin A., Mathematical Research Letters 2020 Vol. 27 No. 3 P. 845-853
We completely solve the inverse Galois problem for del Pezzo surfaces of degree 2 and 3 over all finite fields. ...
Added: October 28, 2020
Rybakov S., Mathematical notes 2016 Vol. 99 No. 3 P. 397-405
Let S be a bielliptic surface over a finite field, and let an elliptic curve B be the Albanese variety of S; then the zeta function of the surface S is equal to the zeta function of the direct product P1 × B. Therefore, the classification problem for the zeta functions of bielliptic surfaces is ...
Added: July 8, 2016
Алешина С. А., Vyugin I. V., Математические заметки 2023 Т. 113 № 1 С. 3-10
We generalize two results in the papers [1:x003] and [2:x003] about sums of subsets of Fp to the more general case in which the sum x+y is replaced by P(x,y), where P is a rather general polynomial. In particular, a lower bound is obtained for the cardinality of the range of P(x,y), where the variables x and y belong to a subgroup G of the multiplicative group of the field Fp. We also prove that ...
Added: January 21, 2023
Galkin S., Rybakov S., / Cornell University. Series math "arxiv.org". 2019. No. 1910.14379.
For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good tower over k=𝔽_{p^2}, that is optimal if p=3. ...
Added: November 6, 2019
Vyugin I. V., Шкредов И. Д., Математический сборник 2012 Т. 203 № 6 С. 81-100
В работе получена оценка мощности множества, полученного пересечением подгруппы мультипликативной группы поля Z_p и нескольких ее аддитивных сдвигов. ...
Added: February 21, 2013
Sergei Valentinovich Fedorenko, / Preprint. Series Preprint "Preprint". 2016.
In this preprint, we present an example illustrating the novel method for the discrete Fourier transform (DFT) computation based on the Goertzel-Blahut algorithm introduced in the paper "Improving the Goertzel-Blahut algorithm" (IEEE Signal Processing Letters, vol. 23, no. 6, pp. 824-827, 2016). ...
Added: February 3, 2018
Nabebin A. A., Tarasikov A. S., M. : -, 2012
The manual contains necessary data from homogeneous and inhomogeneous universal algebras, systems of axioms for the basic algebraic structures (arithmetics, monoids, subgroups, groups, partial ordering, rings, fields). It is described axiomatic programming language OBJ3 with examples of programs in this language. It is intended to students of universities of specialities: the applied mathematics, informatics, computer ...
Added: March 13, 2013
Nabebin A. A., Ученые записки Российского государственного социального университета 2012 № 8 С. 140-147
It is given the group of algorithms providing deciphering of linear feedback shift registers, including the tests for irreducibility and primitiveness of polynomials in a finite field; the test: to be the generator for multiplicative group of a finite field; computing of an inverse element; computing of the sum, product, a natural power of elements; ...
Added: August 28, 2013
V. L. Popov, Doklady Mathematics 2016 Vol. 93 No. 3 P. 307-309
A general theorem on the purity of invariant field extensions is proved. Using it, a criterion of rational triangulability of connected solvable affine algebraic subgroups of the Cremona groups is obtained. This criterion is applied for proving the existence of rationally nontriangulable subgroups of the above form and for proving their stable rational triangulability. The ...
Added: June 29, 2016
NY : Springer, 2013
This volume contains a selection of contributions from the "First International Conference in Network Analysis," held at the University of Florida, Gainesville, on December 14-16, 2011. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The ...
Added: December 19, 2012
Rybakov S., Trepalin A., Математический сборник 2017 Т. 208 № 9 С. 148-170
Пусть X -- минимальная поверхность над полем F_q. Образ Г группы Галуа Gal ( \bar{F_q}, F_q ) в группе автоморфизмов Aut ( Pic X ) является циклической подгруппой группы Вейля W ( E_6 ). В этой подгруппе 25 классов сопряженности циклических подгрупп, и пять из них соответствуют минимальным кубическим поверхностям. Возникает естественный вопрос: какие классы сопряженности ...
Added: October 23, 2017
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017