• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
Of all publications in the section: 12
Sort:
by name
by year
Article
Ayano T., Buchstaber V.M. Chebyshevskii Sbornik. 2020. Vol. 21. No. 1. P. 9-50.

This survey is devoted to the classical and modern problems related to the entire function 𝜎(u; 𝜆), defined by a family of nonsingular algebraic curves of genus 2, where u = (𝑢1, 𝑢3) and 𝜆 = (𝜆4, 𝜆6, 𝜆8, 𝜆10). It is an analogue of the Weierstrass sigma function 𝜎(𝑢; 𝑔2, 𝑔3) of a family of elliptic curves. Logarithmic derivatives of order 2 and higher of the function 𝜎(u; 𝜆) generate fields of hyperelliptic functions of u = (𝑢1, 𝑢3) on the Jacobians of curves with a fixed parameter vector 𝜆. We consider three Hurwitz series 𝜎(u; 𝜆) = ∑︀ 𝑚,𝑛>0 𝑎𝑚,𝑛(𝜆) 𝑢𝑚 1 𝑢 𝑛 3 𝑚!𝑛! , 𝜎(u; 𝜆) = ∑︀ 𝑘>0 𝜉𝑘(𝑢1; 𝜆) 𝑢 𝑘 3 𝑘! and 𝜎(u; 𝜆) = ∑︀ 𝑘>0 𝜇𝑘(𝑢3; 𝜆) 𝑢 𝑘 1 𝑘! . The survey is devoted to the number-theoretic properties of the functions 𝑎𝑚,𝑛(𝜆), 𝜉𝑘(𝑢1; 𝜆) and 𝜇𝑘(𝑢3; 𝜆). It includes the latest results, which proofs use the fundamental fact that the function 𝜎(u; 𝜆) is determined by the system of four heat equations in a nonholonomic frame of six-dimensional space. Keywords: Abelian functions, two-dimensional sigma functions, Hurwitz integrality, generalized Bernoulli—Hurwitz number, heat equation in a nonholonomic frame.

Added: Jun 17, 2021
Article
Vesnin A., Egorov A. Chebyshevskii Sbornik. 2020. Vol. 21. No. 2. P. 65-83.

In this paper we consider a class of right-angled polyhedra in three-dimensional Lobachevsky space, all vertices of which lie on the absolute. New upper bounds on volumes in terms the number of faces of the polyhedron are obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown that the minimum volumes are realized on antiprisms and twisted antiprisms. The first 248 values of volumes of ideal right-angled polyhedra are presented. Moreover,  the class of polyhedra with isolated triangles is introduces and there are obtained combinatorial bounds on their existence as well as minimal examples of such polyhedra are given.

Added: Dec 7, 2020
Article
Иванова О. Ю., Жуков И. Б., Востоков С. В. Чебышевский сборник. 2019. Т. 20. № 2. С. 186-197.

This article links Kurihara’s classification of complete discrete valuation fields and Epp’s theory of elimination of wild ramification. For any complete discrete valuation field K with arbitrary residue field of prime characteristic one can definea certain numerical invariant Γ(K) which underlies Kurihara’s classification of such fields in to 2 types :the field K is of Type I  if ando nlyi f Γ(K) is positive. The value of this invariant indicates how distant is the given field from a standard one, i.e., from a field which is unramified over it sconstant subfield k which is the maximal subfield with perfect residue field. (Standard 2-dimensional local fields are exactly fields of the form k{{t}}.) We prove (under some mild restriction on K) that for a Type I mixed characteristic 2-dimensional local field K there exists an estimate from below for [l:k] wherel /k is an extensions uch that lK is a standard field (existing due to Epp’s theory); the logarithm of this degree can be estimated linearly in terms of Γ(K) with the coefficient depending only on e(K/k).

Added: Nov 13, 2020
Article
Лебедев П. А., Нестеренко А. Ю. Чебышевский сборник. 2012. Т. 13. № 2 (42). С. 91-105.

We consider different parallel algortihms for operations in prime fields and their applications for operations on points of elliptic curves. The work provides results for implementations of these algorithms on NVIDIA graphical processors.

Added: Feb 25, 2013
Article
Рукавишникова М. Г. Чебышевский сборник. 2006. Т. 7. № 4. С. 113-121.

a

Added: Jul 20, 2015
Article
Востоков С., Шашков Т., Афанасьева С. С. Чебышевский сборник. 2020. Т. 21. № 3. С. 39-58.
Added: Apr 19, 2021
Article
Жгун В. С. Чебышевский сборник. 2015. Т. 4. № 56. С. 164-187.
Added: Dec 18, 2015
Article
Жгун В. С. Чебышевский сборник. 2017. Т. 18. № 4. С. 208-220.
Added: Oct 17, 2017
Article
Галатенко А. В., Панкратьев А., Староверов В. Чебышевский сборник. 2021. Т. 22. № 2. С. 76-89.

Quasigroup-based cryptoalgorithms are being actively studied in the framework of theoreticprojects; besides that, a number of quasigroup-based algorithms took part in NIST contestsfor selection of cryptographic standards. From the viewpoint of security it is highly desirableto use quasigroups without proper subquasigroups (otherwise transformations can degrade).We propose algorithms that take a quasigroup specified by the Cayley table as the input anddecide whether there exist proper subquasigroups or subquasigroups of the order at least 2.Temporal complexity of the algorithms is optimized at the cost of increased spatial complexity.We prove bounds on time and memory and analyze the efficiency of software implementationsapplied to quasigroups of a large order. The results were reported at the XVIII InternationalConference «Algebra, Number Theory and Discrete Geometry: modern problems, applicationsand problems of history».

Added: Jun 16, 2021
Article
Чистяков Д. С. Чебышевский сборник. 2017. Т. 18. № 2. С. 256-266.
Added: Oct 10, 2017
Article
Борисов И. М. Чебышевский сборник. 2021. Т. 22. № 1. С. 76-91.

The construction of decomposable curves of degree 8 with multipliers of degrees 3 and 5 is considered in this paper. Sturmfels's modification of Viro's patchworking method for constructing decomposable curves is used. 29 pairwise different curves were constructed.

Added: Apr 18, 2021
Article
Иванова О. Ю., Востоков С. В., Жуков И. Б. Чебышевский сборник. 2019. Т. 20. № 3. С. 124-133.
Added: Nov 13, 2020