Mathematics

On the A. V. Mikhalev’s Problem for Lie Algebras

Authors: Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A.

Weakened A. V. Mikhalev’ sproblem about the prime radical of artinian Lie algebras is solved.

On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields

Authors: Matveev O. A., Matveev V. A.
A condition on summatory function over a set of prime ideals for Dirichlet L-functions on numerical fields is obtained. This condition is equivalent to extended Riemann hypothesis. Analytical properties of Euler products associated with this equivalent are studied

An Estimate of a Certain Summatory Functions Class

Authors: Matveev V. A.
In this paper summatory functions of form P n·x h(n)nit, 1 · |t| · T for finite-valued functions h(n) of natural argument with bounded sum function are estimated

Approximation Polynomials and Dirichlet L-functions Behavior in the Critical Strip

Authors: Matveev O. A.
In this paper a sequence of Dirichlet polynomials that approximate Dirichlet L-functions is constructed. This allows to calculate zeros of L-functions in an effective way and make an assumptions about Dirichlet L-function behavior in the critical strip.

On Universality of Certain Zeta-functions

Authors: Laurinˇcikas A. P., Macaitiene R. .., Mokhov D. .., Siauciunas D. ..
It is well known that a generalization of the Hurwitz zeta-function—the periodic Hurwitz zeta-function with transcendental parameter is universal in the sense that its shifts approximate any analytic function. In the paper, the transcendence condition is replaced by a simpler one on the linear independence of a certain set.

On Combinatorial Problem, Related with Fast Matrix Multiplication

Authors: Kuznetsov Y. V.
The group-theoretical approach to fast matrix multiplication generates specific combinatorial objects, named Uniquely Solvable Puzzles (briefly USP). In the paper some numerical characteristic of the USP was discussed and the relation of USPs to famous combinatorial problem named «Cap set problem» was investigated.

Конгруэнции полигонов над группами

Authors: Халиуллина А. Р.

Получено полное описание конгруэнций полигонов над группами.

On Congruence Lattices of Direct Sums of Strongly Connected Commutative Unary Algebras

Authors: Kartashova A. V.
A union of mutually disjoint unary algebras is called their direct sum. A unary algebra is said to be strongly connected if it is generated by its arbitrary element. In the present paper we investigate congruence lattices of the class of all algebras with finitely many operations whose every connected component is strongly connected. We give a necessary and sufficient condition for an algebra from this class to have a distributive congruence lattice (Theorem 1). Besides, all distributive congruence lattices of algebras from the above class are discribed (Theorem 2).

On Conditions for Distributivity or Modularity of Congruence Lattices of Commutative Unary Algebras

Authors: Kartashov V. K., Kartashova A. V.
The paper is devoted to the problem of describing unary algebras whose congruence lattices have a given property. By now this problem has been solved for algebras with one unary operation. In the paper it is shown that this problem is much more difficult for arbitrary commutative unary algebras. We give some necessary conditions for such lattices to be distributive or modular. Besides, it is proved here that a lattice of all subsets of a set is isomorphic to the congruence lattice of a suitable connected commutative unary algebra.

Some Questions of Number-theoretical Method in Approximation Analysis

Authors: Dobrovolskaya L. P., Dobrovolsky M. N., Dobrovolskii N. M., Rebrova I. Y.
This article gives an overview of several actual problems of optimal coefficients method. This overview was done on September 12, 2013 on XI internation conference «Algebra and number theory: modern problems and applications» in Saratov city.

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