This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers.

Author: Janos Suranyi

Publisher: Springer Science & Business Media

ISBN: 0387953205

Category: Mathematics

Page: 287

View: 145

Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.

Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.

Author: William J. LeVeque

Publisher: Courier Corporation

ISBN: 9780486152080

Category: Mathematics

Page: 496

View: 437

Classic 2-part work now available in a single volume. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes problems and solutions. 1956 edition.

The editors, his students, offer this work as homage to the memory of a great man to whom they, in common with all number theorists, owe a deep and lasting debt.

Author: Hans Rademacher

Publisher: Springer Science & Business Media

ISBN: 9783642806155

Category: Mathematics

Page: 322

View: 595

At the time of Professor Rademacher's death early in 1969, there was available a complete manuscript of the present work. The editors had only to supply a few bibliographical references and to correct a few misprints and errors. No substantive changes were made in the manu script except in one or two places where references to additional material appeared; since this material was not found in Rademacher's papers, these references were deleted. The editors are grateful to Springer-Verlag for their helpfulness and courtesy. Rademacher started work on the present volume no later than 1944; he was still working on it at the inception of his final illness. It represents the parts of analytic number theory that were of greatest interest to him. The editors, his students, offer this work as homage to the memory of a great man to whom they, in common with all number theorists, owe a deep and lasting debt. E. Grosswald Temple University, Philadelphia, PA 19122, U.S.A. J. Lehner University of Pittsburgh, Pittsburgh, PA 15213 and National Bureau of Standards, Washington, DC 20234, U.S.A. M. Newman National Bureau of Standards, Washington, DC 20234, U.S.A. Contents I. Analytic tools Chapter 1. Bernoulli polynomials and Bernoulli numbers ....... . 1 1. The binomial coefficients ..................................... . 1 2. The Bernoulli polynomials .................................... . 4 3. Zeros of the Bernoulli polynomials ............................. . 7 4. The Bernoulli numbers ....................................... . 9 5. The von Staudt-Clausen theorem .............................. . 10 6. A multiplication formula for the Bernoulli polynomials ........... .

One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at the junior or senior level.

Author: Emil Grosswald

Publisher: Springer Science & Business Media

ISBN: 9780817648381

Category: Mathematics

Page: 335

View: 524

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.

" The papers in this volume provide an accurate picture of many of the topics presented at the conference including contributions from four of the plenary lectures.

Author: Scott D. Ahlgren

Publisher: Springer Science & Business Media

ISBN: 9781461303053

Category: Mathematics

Page: 264

View: 205

From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci ence Foundation, The Penn State Conference Center and the Penn State Depart ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. Skinner (Princeton University), "Deformations of Galois representations. " R. Stanley (Massachusetts Institute of Technology), "Some interesting hyperplane arrangements. " F. Rodriguez Villegas (Princeton University), "Modular Mahler measures. " T. Wooley (University of Michigan), "Diophantine problems in many variables: The role of additive number theory. " D. Zeilberger (Temple University), "Reverse engineering in combinatorics and number theory. " The papers in this volume provide an accurate picture of many of the topics presented at the conference including contributions from four of the plenary lectures.

New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.

Author: Benjamin Fine

Publisher: Birkhäuser

ISBN: 9783319438757

Category: Mathematics

Page: 413

View: 564

Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities.

Author: József Sándor

Publisher: Springer Science & Business Media

ISBN: 9781402042157

Category: Mathematics

Page: 622

View: 881

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory.

Author: Henri Cohen

Publisher: Springer Science & Business Media

ISBN: 9781441984890

Category: Mathematics

Page: 581

View: 112

Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.

Author: Gabriel Daniel Villa SalvadorPublish On: 2006-07-11

This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers.

Author: Gabriel Daniel Villa Salvador

Publisher: Springer Science & Business Media

ISBN: 9780817644802

Category: Mathematics

Page: 652

View: 548

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985.

Author: J.S. Chahal

Publisher: Springer Science & Business Media

ISBN: 9781489904393

Category: Mathematics

Page: 191

View: 686

This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. It is intended to be an introduction to the theory of numbers. The audience consisted largely of undergraduate students with no more background than high school mathematics. The presentation was thus kept as elementary and self-contained as possible. However, because the discussion was, generally, carried far enough to introduce the audience to some areas of current research, the book should also be useful to graduate students. The only prerequisite to reading the book is an interest in and aptitude for mathe matics. Though the topics may seem unrelated, the study of diophantine equations has been our main goal. I am indebted to several mathematicians whose published as well as unpublished work has been freely used throughout this book. In particular, the Phillips Lectures at Haverford College given by Professor John T. Tate have been an important source of material for the book. Some parts of Chapter 5 on algebraic curves are, for example, based on these lectures.

However, there is one result from probability theory that requires highlighting. In 1918, Hardy and Ramanujan developed their celebrated circle method to study the partition function. The reader will recall that the number of partitions ...

Author: B. Ramakrishnan

Publisher: Springer Nature

ISBN: 9789811587191

Category: Mathematics

Page: 233

View: 689

This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.

Author: Amir Hossein ParvardiPublish On: 2018-09-11

This challenging book contains fundamentals of elementary number theory as well as a huge number of solved problems and exercises.

Author: Amir Hossein Parvardi

Publisher:

ISBN: 1719920311

Category:

Page: 426

View: 898

This challenging book contains fundamentals of elementary number theory as well as a huge number of solved problems and exercises. The authors, who are experienced mathematical olympiad teachers, have used numerous solved problems and examples in the process of presenting the theory. Another point which has made this book self-contained is that the authors have explained everything from the very beginning, so that the reader does not need to use other sources for definitions, theorems, or problems. On the other hand, Topics in Number Theory introduces and develops advanced subjects in number theory which may not be found in other similar number theory books; for instance, chapter 5 presents Thue's lemma, Vietta jumping, and lifting the exponent lemma (among other things) which are unique in the sense that no other book covers all such topics in one place. As a result, this book is suitable for both beginners and advanced-level students in olympiad number theory, math teachers, and in general whoever is interested in learning number theory.For more information about the book, please refer to https://TopicsInNumberTheory.com.

9 Special topics Number theorists are like lotus-eaters having tasted this food they can never give it up. Leopold Kronecker (1823–1891) 9.1 The harmonic series of prime numbers Theorem 9.1.1. The series ∑ 1 p = 1 2 + 1 3 + 1 5 + 1 7 + ...

Author: Michael Th. Rassias

Publisher: Springer Science & Business Media

ISBN: 9781441904942

Category: Mathematics

Page: 324

View: 994

The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

This work is a collection of original papers presented at an international colloquium on number theory and related topics held at the Tata Institute of Fundamental Research in Bombay.

Author: Richard Askey

Publisher: Oxford University Press

ISBN: UOM:39015060776732

Category: Science

Page: 249

View: 239

This work is a collection of original papers presented at an international colloquium on number theory and related topics held at the Tata Institute of Fundamental Research in Bombay. The papers highlight recent developments in number theory and are dedicated to the memory of Srinivasa Ramanujan, the celebrated Indian mathematician. Topics include Ramanujan's formulas for Eisenstein series, the circle method and the Fourier coefficients of modular forms, linear operators and automorphic forms, exponential Diophantine equations, and others.