New Advances in Transcendence Theory

New Advances in Transcendence Theory PDF

Author: Alan Baker

Publisher: Cambridge University Press

Published: 1988-10-13

Total Pages: 456

ISBN-13: 9780521335454

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This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.

Transcendence Theory, Advances and Applications

Transcendence Theory, Advances and Applications PDF

Author: A. Baker

Publisher:

Published: 1977

Total Pages: 256

ISBN-13:

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This volume is an account of the proceedings of a conference on transcendence theory and its applications held in the University of Cambridge during January and February, 1976. The sixteen papers reflect the considerable current activity in this area, and establish a wide variety of original results. The papers have been arranged in groups with a common themes, such as the theory of linear forms in the logarithms of algebraic numbers and its applications, the transcendence theory of elliptic and Abelian functions, and linear and algebraic independence of meromorphic functions, and arithmetical properties of polynomials in several variables.

Number Theory IV

Number Theory IV PDF

Author: A.N. Parshin

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 351

ISBN-13: 3662036444

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This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.

Number Theory

Number Theory PDF

Author: R.P. Bambah

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 525

ISBN-13: 303487023X

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The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.

Periods And Special Functions In Transcendence

Periods And Special Functions In Transcendence PDF

Author: Tretkoff Paula B

Publisher: World Scientific

Published: 2017-05-04

Total Pages: 228

ISBN-13: 1786342960

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This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on Calabi–Yau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students. It is a nice book for graduate students and researchers interested in transcendence.

Selected Papers on Number Theory and Algebraic Geometry

Selected Papers on Number Theory and Algebraic Geometry PDF

Author: Katsumi Nomizu

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 108

ISBN-13: 9780821804452

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This book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry.

Introduction to Algebraic Independence Theory

Introduction to Algebraic Independence Theory PDF

Author: Yuri V. Nesterenko

Publisher: Springer

Published: 2003-07-01

Total Pages: 257

ISBN-13: 3540445501

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In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.

Elementary and Analytic Theory of Algebraic Numbers

Elementary and Analytic Theory of Algebraic Numbers PDF

Author: Wladyslaw Narkiewicz

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 712

ISBN-13: 3662070014

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This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.

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