An Introduction To Probabilistic Number Theory
DOWNLOAD
Download An Introduction To Probabilistic Number Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get An Introduction To Probabilistic Number Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
An Introduction To Probabilistic Number Theory
DOWNLOAD
Author : Emmanuel Kowalski
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-06
An Introduction To Probabilistic Number Theory written by Emmanuel Kowalski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
Introduction To Analytic And Probabilistic Number Theory
DOWNLOAD
Author : G. Tenenbaum
language : en
Publisher: Cambridge University Press
Release Date : 1995-06-30
Introduction To Analytic And Probabilistic Number Theory written by G. Tenenbaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-30 with Mathematics categories.
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.
Introduction To Analytic And Probabilistic Number Theory
DOWNLOAD
Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-26
Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.
This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews
Mixing Sequences Of Random Variables And Probabilistic Number Theory
DOWNLOAD
Author : Walter Philipp
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Mixing Sequences Of Random Variables And Probabilistic Number Theory written by Walter Philipp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Additive functions categories.
The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Diophantine approximations; discrepancies of sequences uniformly distributed mod one and the distribution of additive functions. In addition to new results, the major contribution of the work is the unification of the listed branches of probabilistic number theory. In particular, this is the first time that the distribution theory of additive functions has been related to metric number theory.
Probabilistic Number Theory I
DOWNLOAD
Author : P.D.T.A. Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probabilistic Number Theory I written by P.D.T.A. Elliott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In 1791 Gauss made the following assertions (collected works, Vol. 10, p.ll, Teubner, Leipzig 1917): Primzahlen unter a (= 00) a la Zahlen aus zwei Factoren lla· a la (warsch.) aus 3 Factoren 1 (lla)2a -- 2 la et sic in info In more modern notation, let 1tk(X) denote the number of integers not exceeding x which are made up of k distinct prime factors, k = 1, 2 ... Then his assertions amount to the asymptotic estimate x (log log X)k-l () 1tk X '"--"';"'-"--"::--:-'-, - (x-..oo). log x (k-1)! The case k = 1, known as the Prime Number Theorem, was independently established by Hadamard and de la Vallee Poussin in 1896, just over a hundred years later. The general case was deduced by Landau in 1900; it needs only an integration by parts. Nevertheless, one can scarcely say that Probabilistic Number Theory began with Gauss. In 1914 the Indian original mathematician Srinivasa Ramanujan arrived in England. Six years of his short life remained to him during which he wrote, amongst other things, five papers and two notes jointly with G.H. Hardy
Probabilistic Number Theory Ii
DOWNLOAD
Author : P.D.T.A. Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probabilistic Number Theory Ii written by P.D.T.A. Elliott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit ably defined independent random variables. This fruiful point of view was intro duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.
Analytic Number Theory An Introductory Course
DOWNLOAD
Author : Paul Trevier Bateman
language : en
Publisher: World Scientific
Release Date : 2004-09-07
Analytic Number Theory An Introductory Course written by Paul Trevier Bateman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Probabilistic Diophantine Approximation
DOWNLOAD
Author : József Beck
language : en
Publisher: Springer
Release Date : 2014-10-06
Probabilistic Diophantine Approximation written by József Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-06 with Mathematics categories.
This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
Probability Theory And Mathematical Statistics
DOWNLOAD
Author : B. Grigelionis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-18
Probability Theory And Mathematical Statistics written by B. Grigelionis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
No detailed description available for "Probability Theory and Mathematical Statistics".
Number Theory With Computations
DOWNLOAD
Author : Peter Shiu
language : en
Publisher: Springer Nature
Release Date : 2024-09-02
Number Theory With Computations written by Peter Shiu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-02 with Mathematics categories.
This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ζ(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.