Complex Analysis In Number Theory
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Complex Analysis In Number Theory
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Author : Anatoly A. Karatsuba
language : en
Publisher: CRC Press
Release Date : 1994-11-22
Complex Analysis In Number Theory written by Anatoly A. Karatsuba and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-22 with Mathematics categories.
This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.
Complex Analysis With Applications To Number Theory
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Author : Tarlok Nath Shorey
language : en
Publisher: Springer Nature
Release Date : 2020-11-13
Complex Analysis With Applications To Number Theory written by Tarlok Nath Shorey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Mathematics categories.
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.
Analytic Number Theory An Introductory Course
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Author : Bateman Paul Trevier
language : en
Publisher: World Scientific
Release Date : 2004-09-07
Analytic Number Theory An Introductory Course written by Bateman Paul Trevier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (”elementary”) and complex variable (”analytic”) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at www.math.uiuc.edu/~diamond/.
Modular Functions And Dirichlet Series In Number Theory
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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modular Functions And Dirichlet Series In Number Theory written by Tom M. Apostol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
Surveys In Number Theory
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-02
Surveys In Number Theory written by Krishnaswami Alladi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-02 with Mathematics categories.
Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).
Number Theory
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Author :
language : en
Publisher:
Release Date : 1975
Number Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Function of complex variables categories.
A View From The Top
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Author : Alex Iosevich
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
A View From The Top written by Alex Iosevich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Combinatorial analysis categories.
Based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.
Explorations In Complex Functions
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Author : Richard Beals
language : en
Publisher: Springer Nature
Release Date : 2020-10-19
Explorations In Complex Functions written by Richard Beals and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-19 with Mathematics categories.
This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.
Complex Analysis And Special Topics In Harmonic Analysis
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Author : Carlos A. Berenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analysis And Special Topics In Harmonic Analysis written by Carlos A. Berenstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.
Eleven Papers On Number Theory Algebra And Functions Of A Complex Variable
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1965-12-31
Eleven Papers On Number Theory Algebra And Functions Of A Complex Variable written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965-12-31 with Mathematics categories.