Periods and Special Functions in Transcendence

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Number Theory

• Author: Paula Tretkoff
• ISBN: 9781786342966
• Publisher: World Scientific Publishing Company
• Publication: May 4, 2017
• Imprint: WSPC (EUROPE)
• Language: English

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.

Contents:

• Preface
• Acknowledgments
• Group Varieties and Transcendence
• Transcendence Results for Exponential and Elliptic Functions
• Modular Functions and Criteria for Complex Multiplication
• Periods of 1-forms on Complex Curves and Abelian Varieties
• Transcendence of Special Values of Hypergeometric Functions
• Transcendence Criterion for Complex Multiplication on K3 Surfaces
• Hodge Structures of Higher Level
• Bibliography
• Index

Readership: Graduate students, researchers.
Key Features:

• It is a lot less technical than most existing books on transcendental number theory
• It provides detailed references for the more difficult transcendence proofs referred in this book
• It provides a great deal of background knowledge on various topics