Mathematics

To the Problem of the Integrity of the Artin’s L-functions

Authors: Kuznetsov V. N., Krivobok V. V., Stepanenko D. S.
In this paper was described a class of Artin’s L-functions, each of which is meromorphic, their poles lays on the critical line Re s = 1/2 and coincides with zeroes of Dedekind’s Z-functions of some fields.

Approximation of Bounded p-variation Periodic Functions by Generalized Abel–Poisson and Logarithmic Means

Authors: Tyuleneva A. A.
An asymptotic estimate of approximation by generalized Abel–Poisson means in p-variation metric on the class of functions with given majorant of p-variational best approximation is proved. Several other quantity results on approximation by these means are
obtained.

An Analogue of the Jordan–Dirichlet Theorem for the Integral Operator with Kernel Having Jumps on Broken Lines

Authors: Koroleva O. A.

In this paper the sufficient conditions (conditions such as Jordan–Dirichlet) expansion function f(x) in a uniformly convergent series of eigenfunctions and associated functions of the integral operator whose kernel is suffering jumps on the sides of the square, inscribed in the unit square. As is known, this expansion requires to f(x) is continuous and belong to the closure of the integral values operator. It turns out that if f(x) also is a function of bounded variation, these conditions are also sufficient.

Determination of the Boundary in the Local Charzynski–Tammi Conjecture for the Fifth Coefficient

Authors: Gordienko V. G., Samsonova K. A.
In this article we find the exact value ofM5 such that the symmetrized Pick function PM4(z) is an extreme in the local Charzynski–
Tammi conjecture for the fifth Taylor coefficient of the normalized holomorphic bounded univalent functions