arXiv subjects
Publications and source records attributed to Ilgar Sh. Jabbarov.
In the paper one proves a necessary condition for divisibility of integral elements by the powers of prime divisor of unramifed prime ideal and gives its application to a simple proof of Fermat's Last Theorem.
In the present paper the asymptotic formulae for the first moment of the Riemann zeta-function on the critical line is proven under assumption of the Riemann Hypothesis.
In this article new bounds for the convergence exponent of the two dimensional Tarry's problem are given.
In the article a new measure in infinite dimensional unite cube different from the Haar or product measures is constructed. Some differences between introduced measure and the product measure are discussed.
In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure introduced in the infinite dimensional unite cube different from the Haar or product measures
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
In this paper we study the mean values and zeroes of Dirichlet series of a view $\sum_{n}a_n n^{-s}$ with complex coefficients. There was introduced some class of Dirichlet series including such widely used series as the Riemann zeta-function, Dirichlet L-functions and ets. A new point of view is introduced in defining of a half plane of mean values. It was proven that in the half plane of mean values any natural degree of the series of an inroduced class, being regular in this half plane,has a mean value. In particular, the analog of Lindelöf Hypothesis is true. If, in addition, the Dirichlet series f(s) belongs to this class with the function f(s)^{-1} then the half plane of mean values was proved to be free from the zeroes.
In this paper The Ergodic Hypothesis is proven for one class of functions defined in the infinite dimensional unite cube where is given an action of some semigroup of mappings without the condition on metric transitivity. The result has not a finite analog.