Elliptic Functions and Transcendence
Author: D.W. Masser
Publisher: Springer
Published: 2006-11-15
Total Pages: 158
ISBN-13: 3540374108
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Periods And Special Functions In Transcendence
Author: Paula B Tretkoff
Publisher: World Scientific
Published: 2017-05-04
Total Pages: 229
ISBN-13: 1786342960
DOWNLOAD EBOOK'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.
The 1-2-3 of Modular Forms
Author: Jan Hendrik Bruinier
Publisher: Springer Science & Business Media
Published: 2008-02-10
Total Pages: 273
ISBN-13: 3540741194
DOWNLOAD EBOOKThis book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Contributions to the Theory of Transcendental Numbers
Author: Gregory Chudnovsky
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 464
ISBN-13: 0821815008
DOWNLOAD EBOOKContains 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.
Elements of the Theory of Elliptic Functions
Author: Naum Ilʹich Akhiezer
Publisher: American Mathematical Soc.
Published: 1990
Total Pages: 237
ISBN-13: 9780821809006
DOWNLOAD EBOOKPresents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.
Transcendental Numbers
Author: M. Ram Murty
Publisher: Springer
Published: 2014-06-24
Total Pages: 219
ISBN-13: 1493908324
DOWNLOAD EBOOKThis book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.
Geometric Topology
Author:
Publisher:
Published: 1975
Total Pages: 459
ISBN-13: 9780387071367
DOWNLOAD EBOOKTranscendental Number Theory
Author: Alan Baker
Publisher: Cambridge University Press
Published: 1990-09-28
Total Pages: 180
ISBN-13: 9780521397919
DOWNLOAD EBOOKFirst published in 1975, this classic book gives a systematic account of transcendental number theory, that is those numbers which cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory enriching many branches of pure mathematics. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalisation of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's |E|-functions and of Sprindzuk's solution to the Mahler conjecture. The volume was revised in 1979: however Professor Baker has taken this further opportunity to update the book including new advances in the theory and many new references.
Transcendence in Algebra, Combinatorics, Geometry and Number Theory
Author: Alin Bostan
Publisher: Springer Nature
Published: 2021-11-02
Total Pages: 544
ISBN-13: 3030843041
DOWNLOAD EBOOKThis proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Surveys in Number Theory
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Published: 2009-03-02
Total Pages: 193
ISBN-13: 0387785108
DOWNLOAD EBOOKNumber 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).
