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Complex Analysis with Applications to Number Theory

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Complex Analysis with Applications to Number Theory/ by Tarlok Nath Shorey.
Author:	Shorey, Tarlok Nath.
Description:	XVI, 287 p. 14 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-981-15-9097-9
ISBN:	9789811590979

Complex Analysis with Applications to Number Theory
Shorey, Tarlok Nath.

Complex Analysis with Applications to Number Theory[electronic resource] /by Tarlok Nath Shorey. - 1st ed. 2020. - XVI, 287 p. 14 illus.online resource. - Infosys Science Foundation Series in Mathematical Sciences,2364-4036. - Infosys Science Foundation Series in Mathematical Sciences,.

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.

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, undergraduate students of engineering and researchers in fields of complex analysis and number theory. This theory is a prerequisite for the study of various areas of mathematics, including the theory of several finitely and infinitely complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. In addition to solved examples and problems, the book covers most topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, Gamma function, and harmonic functions.

ISBN: 9789811590979

Standard No.: 10.1007/978-981-15-9097-9doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Complex Analysis with Applications to Number Theory
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505 0 $a 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.
520 $a 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, undergraduate students of engineering and researchers in fields of complex analysis and number theory. This theory is a prerequisite for the study of various areas of mathematics, including the theory of several finitely and infinitely complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. In addition to solved examples and problems, the book covers most topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, Gamma function, and harmonic functions.
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