› › Periods And Special Functions In Transcendence

Periods And Special Functions In Transcendence

Author : Paula B Tretkoff

Publisher : World Scientific

Page : 229 pages

File Size : 22,8 MB

Release : 2017-05-04

Category : Mathematics

ISBN : 1786342960

Get eBook

Book Description

'The book is mainly addressed to the non-expert reader, in that it assumes only a little background in complex analysis and algebraic geometry, but no previous knowledge in transcendental number theory is required. The technical language is introduced smoothly, and illustrative examples are provided where appropriate … The book is carefully written, and the relevant literature is provided in the list of references. 'Mathematical Reviews ClippingsThis 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.



Periods and Special Functions in Transcendence

Author : Paula Tretkoff

Publisher : Wspc (Europe)

Page : 0 pages

File Size : 29,81 MB

Release : 2017

Category : Hypergeometric functions

ISBN : 9781786342942

Get eBook

Book Description

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.



Transcendence and Linear Relations of 1-Periods

Author : Annette Huber

Publisher : Cambridge University Press

Page : 265 pages

File Size : 36,75 MB

Release : 2022-05-26

Category : Mathematics

ISBN : 1316519937

Get eBook

Book Description

Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.





On Some Applications of Diophantine Approximations

Author : Umberto Zannier

Publisher : Springer

Page : 169 pages

File Size : 11,18 MB

Release : 2015-02-13

Category : Mathematics

ISBN : 8876425209

Get eBook

Book Description

This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.



Arithmetic and Geometry Around Hypergeometric Functions

Author : Rolf-Peter Holzapfel

Publisher : Springer Science & Business Media

Page : 441 pages

File Size : 12,57 MB

Release : 2007-06-28

Category : Mathematics

ISBN : 3764382848

Get eBook

Book Description

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.



Transcendental Number Theory

Author : Alan Baker

Publisher : Cambridge University Press

Page : pages

File Size : 26,82 MB

Release : 2022-06-09

Category : Mathematics

ISBN : 1009229966

Get eBook

Book Description

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.



Surveys in Number Theory

Author : Krishnaswami Alladi

Publisher : Springer Science & Business Media

Page : 193 pages

File Size : 32,66 MB

Release : 2009-03-02

Category : Mathematics

ISBN : 0387785108

Get eBook

Book Description

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

Page : 266 pages

File Size : 47,57 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 1475741146

Get eBook

Book Description

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.



Contributions to the Theory of Transcendental Numbers

Author : Gregory Chudnovsky

Publisher : American Mathematical Soc.

Page : 464 pages

File Size : 12,40 MB

Release : 1984

Category : Mathematics

ISBN : 0821815008

Get eBook

Book Description

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.