Complex analysis with applications to number theory /
Shorey, T. N.,
Complex analysis with applications to number theory / Tarlok Nath Shorey. - Bengalure : Springer Nature, 2020. - 1 online resource (xvi, 287 pages) : illustrations. - Infosys Science Foundation series in mathematical sciences, 2364-4036. . - Infosys Science Foundation series. Mathematical sciences. .
Includes bibliographical references and index.
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.
9789811590979 9811590974
Mathematical analysis.
Number theory.
515 / SHO
Complex analysis with applications to number theory / Tarlok Nath Shorey. - Bengalure : Springer Nature, 2020. - 1 online resource (xvi, 287 pages) : illustrations. - Infosys Science Foundation series in mathematical sciences, 2364-4036. . - Infosys Science Foundation series. Mathematical sciences. .
Includes bibliographical references and index.
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.
9789811590979 9811590974
Mathematical analysis.
Number theory.
515 / SHO