Complex Analysis with Applications to Number Theory
Authors: Shorey, Tarlok Nath
Free Preview- Focuses on interactions of complex analysis with number theorySupplements suitable solved examples and problems with all chaptersIs authored by the winner of the Shanti Swarup Bhatnagar Prize for Science and Technology
Buy this book
- About this Textbook
-
The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics and undergraduate students of engineering, as well as to researchers in complex analysis and number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory. In additional to solved examples and problems, the book covers most of the topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, gamma function and harmonic functions.
- About the authors
-
TARLOK NATH SHOREY is a distinguished professor at the National Institute of Advanced Studies (situated in the campus of the Indian Institute of Science), Bengaluru, India. Earlier, he taught at the Department of Mathematics, Indian Institute of Technology Bombay, India. He also had been associated with the Tata Institute of Fundamental Research (TIFR), Mumbai, India, for a period of 42 years. Professor Shorey has done numerous momentous works on transcendental number theory and Diophantine equation. In 1987, he was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology—the highest science award in India—in the Mathematical Sciences category. He has coauthored a book, Exponential Diophantine Equations, and has more than 142 research publications to his credit. He is fellow of the Indian National Science Academy (INSA), Indian Academy of Sciences (IASc) and The National Academy of Sciences (NASI).
- Table of contents (10 chapters)
-
-
Introduction and Simply Connected Regions
Pages 1-23
-
The Cauchy Theorems and Their Applications
Pages 25-71
-
Conformal Mappings and the Riemann Mapping Theorem
Pages 73-98
-
Harmonic Functions
Pages 99-116
-
The Picard Theorems
Pages 117-132
-
Table of contents (10 chapters)
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Complex Analysis with Applications to Number Theory
- Authors
-
- Tarlok Nath Shorey
- Series Title
- Infosys Science Foundation Series in Mathematical Sciences
- Copyright
- 2020
- Publisher
- Springer Singapore
- Copyright Holder
- Springer Nature Singapore Pte Ltd.
- eBook ISBN
- 978-981-15-9097-9
- DOI
- 10.1007/978-981-15-9097-9
- Hardcover ISBN
- 978-981-15-9096-2
- Series ISSN
- 2364-4036
- Edition Number
- 1
- Number of Pages
- XVI, 287
- Number of Illustrations
- 14 b/w illustrations
- Topics
