Complex Analysis with Applications to Numb...

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Sprache: Englisch

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Beschreibung

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.

Über den 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).

Zusammenfassung

Focuses on interactions of complex analysis with number theory

Supplements suitable solved examples and problems with all chapters

Is authored by the winner of the Shanti Swarup Bhatnagar Prize for Science and Technology

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.

Erscheinungsjahr:	2021
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	304
Reihe:	Infosys Science Foundation Series in Mathematical Sciences
Inhalt:	xvi 287 S. 14 s/w Illustr. 287 p. 14 illus.
ISBN-13:	9789811590993
ISBN-10:	9811590990
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Shorey, Tarlok Nath
Auflage:	1st ed. 2020
Hersteller:	Springer Singapore Springer Nature Singapore Infosys Science Foundation Series in Mathematical Sciences
Maße:	235 x 155 x 17 mm
Von/Mit:	Tarlok Nath Shorey
Erscheinungsdatum:	14.11.2021
Gewicht:	0,464 kg

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