Download or read book Additive Theory of Prime Numbers written by Luogeng Hua and published by American Mathematical Soc.. This book was released on 2009-12-04 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Additive Theory of Prime Numbers by L K Hua Translated from the Chinese by N H Ng written by Lo-kêng Hua and published by . This book was released on 1965 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Theory of Prime Numbers Hua written by Lo-Keng Hua and published by . This book was released on 1965 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive theory of prime numbers written by and published by . This book was released on 1966 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Theory of prime Numbers written by L. K. Hua and published by . This book was released on 1965 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Theory of Prime Numbers written by Loo-Keng Hua (Mathematician, China) and published by . This book was released on 1966 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive theory of prime numbers written by Loo-Keng Hua and published by . This book was released on 1966 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Developments in the Additive Theory of Prime Numbers written by Jianya Liu and published by World Scientific Publishing Company Incorporated. This book was released on 2020-02-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Theory of Prime Numbers written by Hou Loo Keng and published by . This book was released on 1953 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Theory of Prime Numbers written by Warner Berthoff and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Additive Number Theory The Classical Bases written by Melvyn B. Nathanson and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: [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.
Download or read book The Book Of Numbers written by Tianxin Cai and published by World Scientific. This book was released on 2016-08-30 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Natural numbers are the oldest human inventions. This volume describes their nature, laws, history and current status. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. For the first time in history, the Chinese Remainder Theorem is renamed the Qin Jiushao Theorem to give him the full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.In this volume, there is supplementary material after each section to broaden the reader's knowledge and imagination. It either discusses the rudiments of some aspects or introduces new topics, such as the perfect number problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Waring's problem, Catalan's conjecture, Euler's conjecture, Fermat's Last Theorem, etc.Originally published in Chinese as in 2014, The Book of Numbers is written for anyone who loves natural numbers. The author is not only a mathematician, but also a literary and science writer, with more than 20 books published, many of which were translated into 20 languages.
Download or read book The Development of Prime Number Theory written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory written by Wenpeng Zhang and published by Springer Science & Business Media. This book was released on 2006-06-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.
Download or read book Proceedings of The 7th International Conference on Contemporary Education Social Sciences and Humanities Philosophy of Being Human as the Core of Interdisciplinary Research ICCESSH 2022 written by Olga Chistyakova and published by Springer Nature. This book was released on 2023-02-10 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an open access book. The aim of the Conference is to provide a shared platform for academics, scholars, PhD students, and graduate students with different cultural backgrounds to present and discuss research, developments and innovations in the fields of contemporary education, social sciences and humanities are referred with the understanding of the Human being. Papers concerning education, philosophy, philosophical anthropology, sociology, theory and history of culture, epistemology, religions, ethics are strongly related with analyzing of the Human being will be considered. Interdisciplinary approach and comparative perspective are encouraged.
Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Download or read book Number Theory and Its Applications in China written by Yuan Wang and published by American Mathematical Soc.. This book was released on 1988 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.
