Related papers: The Exponential World
We consider transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. Based on their classification in [B3] we investigate their dependence on…
In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a…
Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of $p$--adic continued fractions, i.e. continued…
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
The aim of this thesis is to systematically and consistently study strongly coupled bosonic and fermionic conformal field theories using the large quantum number expansion. The idea behind it is to study sectors of conformal field theories…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
Several recent works suggested the possibility of describing inflation by means of a renormalization group equation. In this paper we discuss the application of these methods to models of quintessence. In this framework a period of…
Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e.…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
The goal of this text is to exhibit some of the ideas and methods from geometric model theory, translated to the particular context of differentially closed fields, exhibiting in a more or less self-contained way the tools needed for the…
The generalized number-theoretic transformation (NPT) is formulated on the basis of the exponential function theorem, which allows us to replace operations modulo the expression as a whole by modulo operations on the exponent of this…