Complex Analysis With Applications To Number Theory

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Complex Analysis with Applications to Number Theory

Tarlok Nath Shorey
Complex Analysis with Applications to Number Theory Book PDF

Author : Tarlok Nath Shorey
Publisher : Springer Nature
Page : 287 pages
File Size : 46,8 Mb
Release : 2020-11-13
Category : Mathematics
ISBN : 9789811590979

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Complex Analysis with Applications to Number Theory by Tarlok Nath Shorey Pdf

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.

Complex Analysis in Number Theory

Anatoly A. Karatsuba
Complex Analysis in Number Theory Book PDF

Author : Anatoly A. Karatsuba
Publisher : CRC Press
Page : 218 pages
File Size : 47,7 Mb
Release : 1994-11-22
Category : Mathematics
ISBN : 0849328667

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Complex Analysis in Number Theory by Anatoly A. Karatsuba Pdf

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

Nakhlé H. Asmar,Loukas Grafakos
Complex Analysis with Applications Book PDF

Author : Nakhlé H. Asmar,Loukas Grafakos
Publisher : Springer
Page : 494 pages
File Size : 52,6 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319940632

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Complex Analysis with Applications by Nakhlé H. Asmar,Loukas Grafakos Pdf

This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications. The text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems. Detailed hints accompany the more challenging problems. Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.

The Prime Number Theorem

G. J. O. Jameson
The Prime Number Theorem Book PDF

Author : G. J. O. Jameson
Publisher : Cambridge University Press
Page : 266 pages
File Size : 48,7 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 0521891108

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The Prime Number Theorem by G. J. O. Jameson Pdf

At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.

Analytic Number Theory: An Introductory Course

Bateman Paul Trevier,Diamond Harold G
Analytic Number Theory An Introductory Course Book PDF

Author : Bateman Paul Trevier,Diamond Harold G
Publisher : World Scientific
Page : 376 pages
File Size : 48,7 Mb
Release : 2004-09-07
Category : Mathematics
ISBN : 9789814365567

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Analytic Number Theory: An Introductory Course by Bateman Paul Trevier,Diamond Harold G Pdf

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/.

Complex Analysis and Applications

Hemant Kumar Pathak
Complex Analysis and Applications Book PDF

Author : Hemant Kumar Pathak
Publisher : Unknown
Page : 928 pages
File Size : 47,5 Mb
Release : 2019
Category : Functions of complex variables
ISBN : 981139735X

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Complex Analysis and Applications by Hemant Kumar Pathak Pdf

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog's theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz's rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.

Complex Analysis

Eberhard Freitag,Rolf Busam
Complex Analysis Book PDF

Author : Eberhard Freitag,Rolf Busam
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 51,6 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783540308232

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Complex Analysis by Eberhard Freitag,Rolf Busam Pdf

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

Modular Functions and Dirichlet Series in Number Theory

Tom M. Apostol
Modular Functions and Dirichlet Series in Number Theory Book PDF

Author : Tom M. Apostol
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209997

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Modular Functions and Dirichlet Series in Number Theory by Tom M. Apostol Pdf

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.

Introductory Complex Analysis

Richard A. Silverman
Introductory Complex Analysis Book PDF

Author : Richard A. Silverman
Publisher : Courier Corporation
Page : 402 pages
File Size : 52,7 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318523

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Introductory Complex Analysis by Richard A. Silverman Pdf

Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Complex Analysis and Applications

Hemant Kumar Pathak
Complex Analysis and Applications Book PDF

Author : Hemant Kumar Pathak
Publisher : Springer Nature
Page : 928 pages
File Size : 50,6 Mb
Release : 2019-08-19
Category : Mathematics
ISBN : 9789811397349

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Complex Analysis and Applications by Hemant Kumar Pathak Pdf

This book offers an essential textbook on complex analysis. After introducing the theory of complex analysis, it places special emphasis on the importance of Poincare theorem and Hartog’s theorem in the function theory of several complex variables. Further, it lays the groundwork for future study in analysis, linear algebra, numerical analysis, geometry, number theory, physics (including hydrodynamics and thermodynamics), and electrical engineering. To benefit most from the book, students should have some prior knowledge of complex numbers. However, the essential prerequisites are quite minimal, and include basic calculus with some knowledge of partial derivatives, definite integrals, and topics in advanced calculus such as Leibniz’s rule for differentiating under the integral sign and to some extent analysis of infinite series. The book offers a valuable asset for undergraduate and graduate students of mathematics and engineering, as well as students with no background in topological properties.

Complex Analysis

Serge Lang
Complex Analysis Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 55,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475718713

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Complex Analysis by Serge Lang Pdf

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Surveys in Number Theory

Krishnaswami Alladi
Surveys in Number Theory Book PDF

Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 52,9 Mb
Release : 2009-03-02
Category : Mathematics
ISBN : 9780387785103

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Surveys in Number Theory by Krishnaswami Alladi Pdf

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).

A First Course in Complex Analysis with Applications

Dennis Zill,Patrick Shanahan
A First Course in Complex Analysis with Applications Book PDF

Author : Dennis Zill,Patrick Shanahan
Publisher : Jones & Bartlett Learning
Page : 471 pages
File Size : 43,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763757724

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A First Course in Complex Analysis with Applications by Dennis Zill,Patrick Shanahan Pdf

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Complex Variables with Applications

Saminathan Ponnusamy,Herb Silverman
Complex Variables with Applications Book PDF

Author : Saminathan Ponnusamy,Herb Silverman
Publisher : Springer Science & Business Media
Page : 521 pages
File Size : 48,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9780817645137

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Complex Variables with Applications by Saminathan Ponnusamy,Herb Silverman Pdf

Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students

Complex Analysis with Applications in Science and Engineering

Harold Cohen
Complex Analysis with Applications in Science and Engineering Book PDF

Author : Harold Cohen
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 48,7 Mb
Release : 2010-04-23
Category : Mathematics
ISBN : 9780387730585

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Complex Analysis with Applications in Science and Engineering by Harold Cohen Pdf

The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation.