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Complex Analysis with Applications to Number Theory

BuchGebunden
287 Seiten
Englisch
Springererschienen am14.11.20201st ed. 2020
The book discusses major topics in complex analysis with applications to 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.mehr
Verfügbare Formate
BuchGebunden
EUR32,09
BuchKartoniert, Paperback
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E-BookPDF1 - PDF WatermarkE-Book
EUR50,28

Produkt

KlappentextThe book discusses major topics in complex analysis with applications to 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.

Inhalt/Kritik

Inhaltsverzeichnis
Introduction And Preliminaries.- Cauchy Theorems and Their Applications.-  Conformal Mappings and Riemann Mapping Theorem.- Picard's Theorems.- Factorisation of Analytic Functions in C and in a Region.- Gamma Function.- Riemann Zeta Function.- Dirichlet Series and Dirichlet Theorem.- Harmonic Functions.- Elliptic Functions and Modular Forms.mehr
Kritik
"This book covers essential materials of complex analysis and contains special topics on number theory. ... This book is elegantly written and self-contained with rigorous proofs. It is an attractive introductory book for those who are interested in not only complex analysis but also analytic number theory." (Jongho Yang, Mathematical Reviews, April, 2022)

"The strength of this text is in its concise but complete development of each topic. ... Shorey's text is best used for a second complex analysis course covering a range of advanced topics ... ." (Ian Whitehead, MAA Reviews, January 10, 2022)
"The book can serve as a reference source for readers interested in mathematical relations between complex analysis and number theory. Also, it can attract amateurs of classical conjectures for the Riemann zeta function." (Dmitri V. Prokhorov, zbMATH 1467.30001, 2021)mehr

Autor

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).
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Shorey, Tarlok Nath