Elliptic Functions and Transcendence
Author: D.W. Masser
Publisher: Springer
Published: 2006-11-15
Total Pages: 158
ISBN-13: 3540374108
DOWNLOAD EBOOK →Lanterna Rally
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Geometric Topology
Transcendence Theory, Advances and Applications
Author: A. Baker
Publisher:
Published: 1977
Total Pages: 256
ISBN-13:
DOWNLOAD EBOOK →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.
Periods And Special Functions In Transcendence
Author: Tretkoff Paula B
Publisher: World Scientific
Published: 2017-05-04
Total Pages: 228
ISBN-13: 1786342960
DOWNLOAD EBOOK →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.
Contributions to the Theory of Transcendental Numbers
Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 464
ISBN-13: 0821815008
DOWNLOAD EBOOK →Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.
Transcendence Methods
Author: Michel Waldschmidt
Publisher: Kingston, Ont. : Queen's Univeristy
Published: 1979
Total Pages: 158
ISBN-13:
DOWNLOAD EBOOK →Surveys in Number Theory
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Published: 2009-03-02
Total Pages: 193
ISBN-13: 0387785108
DOWNLOAD EBOOK →Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).
Making Transcendence Transparent
Author: Edward B. Burger
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 266
ISBN-13: 1475741146
DOWNLOAD EBOOK →This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.
Pillars of Transcendental Number Theory
Author: Saradha Natarajan
Publisher: Springer Nature
Published: 2020-05-02
Total Pages: 184
ISBN-13: 9811541558
DOWNLOAD EBOOK →This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite–Lindemann–Weierstrass theorem, Gelfond–Schneider theorem, Schmidt’s subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker’s original results. This book presents Baker’s original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of “Exercises” and interesting information presented as “Notes,” intended to spark readers’ curiosity.
Introduction to Algebraic Independence Theory
Author: Yuri V. Nesterenko
Publisher: Springer
Published: 2003-07-01
Total Pages: 257
ISBN-13: 3540445501
DOWNLOAD EBOOK →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.
