A. Laurinčikas

Замечания об универсальности периодической дзета-функции@@@Remarks on the universality of the periodic zeta function

We present an universality theorem for the periodic zeta-function which is definedby a Dirichlet series withperiodic coefficients satisfying a certain dependence condition. This simplifies the problem and allows to elucidate the universalityof theperiodic zeta-function.

On the Periodic Zeta-Function

We consider the periodic zeta-function introduced by B. C. Berndt and L. Schoenfeld. We obtain the asymptotics of the mean square and prove limit theorems in the space of analytic functions for this function.

An Approximate Functional Equation for the Lerch Zeta Function

In this paper, we establish an approximate functional equation for the Lerch zeta function, which is a generalization of the Riemann zeta function and the Hurwitz zeta function.

A Joint Limit Theorem for General Dirichlet Series

We obtain a joint limit theorem in the sense of weak convergence of probability measures for general Dirichlet series in the space of meromorphic functions.

An Elliott-type theorem for twists of L-functions of elliptic curves

A limit theorem involving an increasing modulus of the character is obtained for twists with the Dirichlet character of L-functions of elliptic curves.

Sharpening of the universality inequality

The universality theoremasserts that the lower density of any set of shifts of the Riemann zeta-function which approximate a given analytic function with accuracy ɛ > 0 is strictly positive. It is proved that this set has strictly positive density for all but at most countably many ɛ > 0.

On Zeta-Functions of Finite Abelian Groups

In the paper, the zeta-functions of finite Abelian groups of rank 2 and 3 are considered. One- and two-dimensional limit theorems for these zeta-functions on the complex plane and in the space of meromorphic functions are obtained.

Universality theorems for zeta-functions with periodic coefficients

We obtain Voronin-type universality theorems for some classes of functions of a collection of periodic zeta-functions and periodic Hurwitz zeta-functions with algebraically independent parameters.

A growth estimate for the Mellin transform of the Riemann zeta function

In this paper, we obtain an upper bound for the modified Mellin transform of the Riemann zeta function on the critical strip.

A remark on negative moments of the Riemann zeta-function

With the use of the boundedness condition, the asymptotics of negative moments of the normalized Riemann zeta-function is obtained.