Related papers: Periods And Real Numbers
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity.
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the…
Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values…
A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period…
We introduce the concept of degree to classify the periods in the sense of Kontsevich. Using this notion we give some new understanding of some problems in transcendental number theory.
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…
This article provides a brief introductory account of the theory of aperiodic order.
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
The periods, introduced by Kontsevich and Zagier, form a class of complex numbers which contains all algebraic numbers and several transcendental quantities. Little has been known about qualitative properties of periods. In this paper, we…
This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal…
We define the period as a multiplicative characteristic of stably symmetric monoidal $\infty$-categories, develop its basic properties, and study many examples, with a focus on `ordinary' equivariant and motivic homotopy theory. We apply…