New Developments In The Additive Theory Of Prime Numbers
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New Developments In The Additive Theory Of Prime Numbers
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Author : Jianya Liu
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2020-02-28
New Developments In The Additive Theory Of Prime Numbers written by Jianya Liu and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Mathematics categories.
The Development Of Prime Number Theory
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Development Of Prime Number Theory written by Wladyslaw Narkiewicz 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 2013-03-14 with Mathematics categories.
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Additive Theory Of Prime Numbers
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Author : Luogeng Hua
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-12-04
Additive Theory Of Prime Numbers written by Luogeng Hua 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 2009-12-04 with Mathematics categories.
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.
Developments In Language Theory
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Author : Mizuho Hoshi
language : en
Publisher: Springer
Release Date : 2018-09-03
Developments In Language Theory written by Mizuho Hoshi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Computers categories.
This book constitutes the proceedings of the 22nd International Conference on Developments in Language Theory, DLT 2018, held in Tokyo, Japan, in September 2018. The 39 full papers presented in this volume were carefully reviewed and selected from 84 submissions. The papers cover the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphics, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis, polyominoes and bidimensional patterns; cryptography; concurrency; celluar automata; bio-inspired computing; quantum computing.
Current Trends In Symmetric Polynomials With Their Applications
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Author : Taekyun Kim
language : en
Publisher: MDPI
Release Date : 2021-03-19
Current Trends In Symmetric Polynomials With Their Applications written by Taekyun Kim and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-19 with Mathematics categories.
The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.
Collected Papers Of Hans Rademacher
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Author : Hans Rademacher
language : en
Publisher: MIT Press
Release Date : 1974
Collected Papers Of Hans Rademacher written by Hans Rademacher and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Business & Economics categories.
Hans Adolph Rademacher was a German-born American mathematician, known for work in mathematical analysis and number theory.
New Trends In Probability And Statistics
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Author : Fritz Schweiger
language : en
Publisher: VSP
Release Date : 1992
New Trends In Probability And Statistics written by Fritz Schweiger and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
Rational Number Theory In The 20th Century
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Author : Władysław Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-02
Rational Number Theory In The 20th Century written by Władysław Narkiewicz 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 2011-09-02 with Mathematics categories.
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Ergodic Theory And Dynamical Systems In Their Interactions With Arithmetics And Combinatorics
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Author : Sébastien Ferenczi
language : en
Publisher: Springer
Release Date : 2018-06-15
Ergodic Theory And Dynamical Systems In Their Interactions With Arithmetics And Combinatorics written by Sébastien Ferenczi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-15 with Mathematics categories.
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Dynamical Systems Number Theory And Applications
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Author : Thomas Hagen
language : en
Publisher: World Scientific
Release Date : 2016
Dynamical Systems Number Theory And Applications written by Thomas Hagen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
"This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions."--