Additive Theory Of Prime Numbers

Author : Luogeng Hua
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 41,6 Mb
Release : 2009-12-04
Category : Mathematics
ISBN : 9780821849422

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Additive Theory of Prime Numbers by Luogeng Hua Pdf

Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.

Author : Anonim
Publisher : Unknown
Page : 190 pages
File Size : 43,9 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:927533256

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Additive theory of prime numbers by Anonim Pdf

Author : Jianya Liu,Tao Zhan
Publisher : World Scientific Publishing Company Incorporated
Page : 200 pages
File Size : 55,6 Mb
Release : 2020-02-28
Category : Mathematics
ISBN : 9812775927

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New Developments in the Additive Theory of Prime Numbers by Jianya Liu,Tao Zhan Pdf

Author : Loo-Keng Hua
Publisher : Unknown
Page : 190 pages
File Size : 42,6 Mb
Release : 1966
Category : Electronic
ISBN : OCLC:927533256

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Additive theory of prime numbers by Loo-Keng Hua Pdf

Author : Lo-Keng Hua
Publisher : Unknown
Page : 13 pages
File Size : 40,5 Mb
Release : 1965
Category : Electronic
ISBN : OCLC:559631111

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Additive Theory of Prime Numbers. Hua by Lo-Keng Hua Pdf

Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 45,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475738452

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Additive Number Theory The Classical Bases by Melvyn B. Nathanson Pdf

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

Author : Lo-kêng Hua
Publisher : Unknown
Page : 190 pages
File Size : 44,6 Mb
Release : 1965
Category : Numbers, Prime
ISBN : OCLC:977417459

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Additive Theory of Prime Numbers, by L.K. Hua. [Translated from the Chinese by N.H. Ng]. by Lo-kêng Hua Pdf

Author : Gove W. Effinger,David R. Hayes
Publisher : Unknown
Page : 184 pages
File Size : 52,8 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015022029501

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Additive Number Theory of Polynomials Over a Finite Field by Gove W. Effinger,David R. Hayes Pdf

This book helps gather the sum of additive number theory.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 743 pages
File Size : 46,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400903654

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : S.D. Adhikari,B. Ramakrishnan
Publisher : Springer
Page : 285 pages
File Size : 42,5 Mb
Release : 2009-06-15
Category : Mathematics
ISBN : 9789386279460

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Number Theory and Applications by S.D. Adhikari,B. Ramakrishnan Pdf

This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

Author : Stanisław Krajewski,Stephen Krajewski
Publisher : IOS Press
Page : 380 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : 1586038141

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Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science by Stanisław Krajewski,Stephen Krajewski Pdf

This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.

Author : Anonim
Publisher : Cambridge University Press
Page : 248 pages
File Size : 53,6 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9780521573474

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The Hardy-Littlewood Method by Anonim Pdf

Author : Chaohua Jia,Kohji Matsumoto
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 44,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475736212

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Analytic Number Theory by Chaohua Jia,Kohji Matsumoto Pdf

From September 13 to 17 in 1999, the First China-Japan Seminar on Number Theory was held in Beijing, China, which was organized by the Institute of Mathematics, Academia Sinica jointly with Department of Mathematics, Peking University. TE:m Japanese Professors and eighteen Chinese Professors attended this seminar. Professor Yuan Wang was the chairman, and Professor Chengbiao Pan was the vice-chairman. This seminar was planned and prepared by Professor Shigeru Kanemitsu and the first-named editor. Talks covered various research fields including analytic number theory, algebraic number theory, modular forms and transcendental number theory. The Great Wall and acrobatics impressed Japanese visitors. From November 29 to December 3 in 1999, an annual conference on analytic number theory was held in Kyoto, Japan, as one of the conferences supported by Research Institute of Mathematical Sciences (RIMS), Kyoto University. The organizer was the second-named editor. About one hundred Japanese scholars and some foreign visitors com ing from China, France, Germany and India attended this conference. Talks covered many branches in number theory. The scenery in Kyoto, Arashiyama Mountain and Katsura River impressed foreign visitors. An informal report of this conference was published as the volume 1160 of Surikaiseki Kenkyusho Kokyuroku (June 2000), published by RIMS, Ky oto University. The present book is the Proceedings of these two conferences, which records mainly some recent progress in number theory in China and Japan and reflects the academic exchanging between China and Japan.

Author : Anatoliĭ Alekseevich Karat︠s︡uba,V. I. Blagodatskikh
Publisher : American Mathematical Soc.
Page : 366 pages
File Size : 44,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0821804677

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Number Theory and Analysis by Anatoliĭ Alekseevich Karat︠s︡uba,V. I. Blagodatskikh Pdf

"This collection consists of papers ... devoted to current trends in analytic number theory, function theory, algebraic number theory, algebraic geometry, and combinatorics" -- t.p. verso.

Author : John Forbes Nash, Jr.,Michael Th. Rassias
Publisher : Springer
Page : 543 pages
File Size : 52,8 Mb
Release : 2016-07-05
Category : Mathematics
ISBN : 9783319321622

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Open Problems in Mathematics by John Forbes Nash, Jr.,Michael Th. Rassias Pdf

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.