Complex Analysis with Applications to Number Theory

✍ Scribed by Tarlok Nath Shorey

• Publisher: Springer Singapore;Springer
• Year: 2020
• Tongue: English
• Leaves: 297
• Series: Infosys Science Foundation Series
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xvi
Introduction and Simply Connected Regions (Tarlok Nath Shorey)....Pages 1-23
The Cauchy Theorems and Their Applications (Tarlok Nath Shorey)....Pages 25-71
Conformal Mappings and the Riemann Mapping Theorem (Tarlok Nath Shorey)....Pages 73-98
Harmonic Functions (Tarlok Nath Shorey)....Pages 99-116
The Picard Theorems (Tarlok Nath Shorey)....Pages 117-132
The Weierstrass Factorisation Theorem, Hadamard’s Factorisation Theorem and the Gamma Function (Tarlok Nath Shorey)....Pages 133-185
The Riemann Zeta Function and the Prime Number Theorem (Tarlok Nath Shorey)....Pages 187-236
The Prime Number Theorem with an Error Term (Tarlok Nath Shorey)....Pages 237-250
The Dirichlet Series and the Dirichlet Theorem on Primes in Arithmetic Progressions (Tarlok Nath Shorey)....Pages 251-269
The Baker Theorem (Tarlok Nath Shorey)....Pages 271-281
Back Matter ....Pages 283-287

✦ Subjects

Mathematics; Analysis; Number Theory