Universality for <Emphasis Type="Italic">L</Emphasis>-functions in the Selberg class

We prove universality for L-functions L \mathcal{L} from the Selberg class satisfying some mild condition on the Dirichlet coefficients (which might be considered as a prime number theorem for L \mathcal{L} ). This generalizes a previous universality theorem by the second author, where the L-function was assumed to have a polynomial Euler product satisfying the Ramanujan hypothesis.     

Computing the values of <Emphasis Type=Italic>L</Emphasis>-functions,and the chebyshev polynomials

The Chebyshev polynomials and Chebyshev’s economization method are applied to speed up the computation of the values of L-functions. Bibliography: 3 titles.     

Values of Dirichlet <Emphasis Type=Italic>L</Emphasis>-functions,Gauss sums and trigonometric sums

Motivated by the classical work of Ramanujan and recent work of Berndt and Zaharescu, we establish certain infinite families of identities relating values of Dirichlet L-functions at positive integers to Gauss sums and trigonometric sums twisted with characters.     

On the distribution of the zeros of the cubic <Emphasis Type=Italic>L</Emphasis>-function

The distribution of the real parts of the zeros of the cubic L-function is considered. Some observations based on numerical results are presented. Bibliography: 4 titles.     

Nonlocal General Boundary Value Problems of Elliptic Type in <Emphasis Type=Italic>L</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript> Cases

This paper is devoted to the study of operational second-order differential equations of elliptic type with nonregular coefficient-operator boundary conditions. In the framework of UMD spaces, we give some new results by using semi-groups and interpolation theory. We define two types of solutions: semi-strict and strict solutions. We then characterizes the existence and uniqueness of such solutions.     

About the computation of the signature of surface singularities <Emphasis Type=Italic>z</Emphasis><Superscript><Emphasis Type=Italic>N</Emphasis></Superscript> + <Emphasis Type=Italic>g</Emphasis>(<Emphasis Type=Italic>x,y</Emphasis>) = 0

In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z ^N + g(x; y) = 0.     

On the mean value of the generalized Dirichlet <Emphasis Type="Italic">L</Emphasis>-functions

Let q ⩾ 3 be an integer, let χ denote a Dirichlet character modulo q. For any real number a ⩾ 0 we define the generalized Dirichlet L-functions

Transcendental values of class group <Emphasis Type="Italic">L</Emphasis>-functions

Let K be an algebraic number field and f a complex-valued function on the ideal class group of K. Then, f extends in a natural way to the set of all non-zero ideals of the ring of integers of K and we can consider the Dirichlet series \({L(s,f) =\sum_{{\mathfrak a}} f({\mathfrak a}){\bf N}({\mathfrak a})^{-s}}\) which converges for \({{\mathfrak R}(s) >1 }\). After extending this function to \({{\mathfrak R}(s)=1}\), and in the case that f does not contain the trivial character, we study the special value L(1, f) when f is algebraic valued and K is an imaginary quadratic field. Applying Kronecker’s limit formula and Baker’s theory of linear forms in logarithms, we derive a variety of results related to the transcendence of this special value.     

Value-distribution of twisted automorphic <Emphasis Type="Italic">L</Emphasis>-functions

In this paper, we prove a limit theorem for twisted with character automorphic L-functions with an increasing modulus of the character.     

The <Emphasis Type="Italic">L</Emphasis>-functions of Witt coverings

Results on L-functions of Artin–Schreier coverings by Dwork, Bombieri and Adolphson–Sperber are generalized to L-functions of Witt coverings.     

About <Emphasis Type=Italic>I</Emphasis>(<Emphasis Type=Italic>J</Emphasis>)-approximately continuous functions

A generalization of density point with respect to category and I(J)-density topology has been presented in [5]. This papers deals with some basic properties of the corresponding I(J)-approximately continuous functions and gives answer when these functions are of the first Baire class and when they are Darboux functions.     

Radicals of <Emphasis Type=Italic>l</Emphasis>-rings and one-sided <Emphasis Type=Italic>l</Emphasis>-ideals

We consider the plane deformation of an infinite body with a cylindrical inclusion whose mechanical and thermophysical characteristics differ from those of the material of the body for a heat flow and tensile forces given far from the inclusion. Stress intensity factors in the vicinity of a crack located on the continuation of the diameter of the inclusion are determined by the solution of a singular integral equation using the method of mechanical quadratures. We investigate the ratio of the length of the crack to the distance between it and the inclusion at which the regular kernel of the integral equation can be neglected in calculations. In this case, analytic formulas for the determination of the stress intensity factors are obtained.