Multiplicative Number Theory I
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Multiplicative Number Theory
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Author : H. Davenport
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Multiplicative Number Theory written by H. Davenport 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 2013-06-29 with Mathematics categories.
Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.
Multiplicative Number Theory I
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Author : Hugh L. Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2007
Multiplicative Number Theory I written by Hugh L. Montgomery 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 2007 with Mathematics categories.
A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Handbook Of Number Theory I
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Author : József Sándor
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-17
Handbook Of Number Theory I written by József Sándor 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 2005-11-17 with Mathematics categories.
This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.
Number Theory I
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Author : Yu. I. Manin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Number Theory I written by Yu. I. Manin 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 2013-04-17 with Mathematics categories.
Preface Among the various branches of mathematics, number theory is characterized to a lesser degree by its primary subject ("integers") than by a psychologi cal attitude. Actually, number theory also deals with rational, algebraic, and transcendental numbers, with some very specific analytic functions (such as Dirichlet series and modular forms), and with some geometric objects (such as lattices and schemes over Z). The question whether a given article belongs to number theory is answered by its author's system of values. If arithmetic is not there, the paper will hardly be considered as number-theoretical, even if it deals exclusively with integers and congruences. On the other hand, any mathematical tool, say, homotopy theory or dynamical systems may become an important source of number-theoretical inspiration. For this reason, com binatorics and the theory of recursive functions are not usually associated with number theory, whereas modular functions are. In this report we interpret number theory broadly. There are compelling reasons to adopt this viewpoint. First of all, the integers constitute (together with geometric images) one of the primary subjects of mathematics in general. Because of this, the history of elementary number theory is as long as the history of all mathematics, and the history of modern mathematic began when "numbers" and "figures" were united by the concept of coordinates (which in the opinion of LR. Shafarevich also forms the basic idea of algebra).
Probabilistic Number Theory I
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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
Equidistribution In Number Theory An Introduction
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Author : Andrew Granville
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-08
Equidistribution In Number Theory An Introduction written by Andrew Granville 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 2007-04-08 with Mathematics categories.
From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series “Seminaire ́ de mathematiques ́ superieures”, ́ was held at the U- versite ́ de Montreal, ́ on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have noticed incre- ing interest being paid to distribution problems, whether of rational points, of zeros of zeta functions, of eigenvalues, etc. Although these problems have been motivated from very di?erent perspectives, one nds that there is much in common, and presumably it is healthy to try to view such questions as part of a bigger subject. It is for this reason we decided to hold a school on “Equidistribution in number theory” to introduce junior researchers to these beautiful questions, and to determine whether di?erent approaches can in uence one another. There are far more good problems than we had time for in our schedule. We thus decided to focus on topics that are clearly inter-related or do not requirealotofbackgroundtounderstand.
Analytic Number Theory
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Author : Carl Pomerance
language : en
Publisher: Springer
Release Date : 2015-11-18
Analytic Number Theory written by Carl Pomerance and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Mathematics categories.
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.
A Comprehensive Course In Number Theory
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Author : Alan Baker
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-23
A Comprehensive Course In Number Theory written by Alan Baker 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 2012-08-23 with Computers categories.
The author's classic concise introduction now fully updated and developed to suit courses extending from primers to introductions to research.
Analytic Number Theory Modular Forms And Q Hypergeometric Series
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Author : George E. Andrews
language : en
Publisher: Springer
Release Date : 2018-02-01
Analytic Number Theory Modular Forms And Q Hypergeometric Series written by George E. Andrews and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Cryptanalysis Of Number Theoretic Ciphers
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Author : Samuel S. Wagstaff, Jr.
language : en
Publisher: CRC Press
Release Date : 2019-08-22
Cryptanalysis Of Number Theoretic Ciphers written by Samuel S. Wagstaff, Jr. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.
At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.