Related papers: Development of a complex function theory upon a ne…

We define the algebra of Colombeau generalized functions on a subset A of the space of d-dimensional generalized points. If the domain A is open, such generalized functions can be identified with pointwise maps from A into the ring of…

The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…

We give an algebraic analog of the functional equation of Riemann's theta function. More precisely, we define a `theta multiplier' line bundle over the moduli stack of principally polarized abelian schemes with theta characteristic and…

We generalize the construction of affine polar graphs in two different ways to obtain new partial difference sets and amorphic association schemes. The first generalization uses a combination of quadratic forms and uniform cyclotomy. In the…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl groups with respect to the…

This paper is a companion paper to [G4], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [G4] are stated in a rather general…

The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…

The present essay aims at investigating whether and how far an algebraic analysis of the Zeta Function and of the Riemann Hypothesis can be carried out. Of course the well-established properties of the Zeta Function, explored in depth in…

We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we show that a non-commutative function has a matrix-centre…

In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration (this condition is a generalization of the classical relation 1 + i^2 = 0 in…

This is a review paper based on the series of our papers devoted to a structure of true-poly-analytic Bergman function spaces over the upper half-plane in the complex plane and to a detailed study of properties of Toeplitz operators with…

These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…

We introduce and study new versions of polylogarithms and a zeta function on a completion of $\mathbb F_q (x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for $\mathbb F_q$-linear functions.

We study non-analytic terms, which cannot be written in the form of any positive integer power of field-dependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

In the introduction part of this paper, first of all, the concept of absolute integral sum of complex function is defined, as more general one with respect to the concept of integral as well as of integral sum of "ordinary'' integral…

We introduce formulas for the logarithms of Drinfeld modules using a framework recently developed by the second author. We write the logarithm function as the evaluation under a motivic map of a product of rigid analytic trivializations of…

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…