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Representations Of Integers As Sums Of Squares
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Book Synopsis Representations of Integers as Sums of Squares by : E. Grosswald
Download or read book Representations of Integers as Sums of Squares written by E. Grosswald and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con sisted of particularly gifted and eager listeners; unfortunately, their back ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.
Book Synopsis Sums of Squares of Integers by : Carlos J. Moreno
Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's element
Book Synopsis Representations of Integers as Sums of Squares by : Timothy Atwill
Download or read book Representations of Integers as Sums of Squares written by Timothy Atwill and published by . This book was released on 1989 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of Integers as Sums of Squares by : Emil Grosswald
Download or read book Representations of Integers as Sums of Squares written by Emil Grosswald and published by . This book was released on 1985-01-01 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Representation of Integers as Sums of Two, Three and Four Squares by : Thyrsa Anne Frazier
Download or read book The Representation of Integers as Sums of Two, Three and Four Squares written by Thyrsa Anne Frazier and published by . This book was released on 1952 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sums of Squares of Integers by : Carlos J. Moreno
Download or read book Sums of Squares of Integers written by Carlos J. Moreno and published by CRC Press. This book was released on 2005-12-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Book Synopsis Representation of Integers as Sum of Squares by : Rashidah Ismail
Download or read book Representation of Integers as Sum of Squares written by Rashidah Ismail and published by . This book was released on 1989 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Representation of an Integer as the Sum of Squares by : Manwah Lilian Wong
Download or read book On the Representation of an Integer as the Sum of Squares written by Manwah Lilian Wong and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Representation of Integers as the Sum of Three Squares by : Donald Ian Morrison
Download or read book The Representation of Integers as the Sum of Three Squares written by Donald Ian Morrison and published by . This book was released on 1952 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representations of integers as sums of Fibonacci squares by : Roger D. O?Connell
Download or read book Representations of integers as sums of Fibonacci squares written by Roger D. O?Connell and published by . This book was released on 1970 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Number of Representations of the Square of an Integer as the Sum of an Odd Number of Squares by : Carl Douglas Olds
Download or read book On the Number of Representations of the Square of an Integer as the Sum of an Odd Number of Squares written by Carl Douglas Olds and published by . This book was released on 1940 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Book Synopsis On Representations of a Positive Integer as a Sum of Squares by : C. P. Smith
Download or read book On Representations of a Positive Integer as a Sum of Squares written by C. P. Smith and published by . This book was released on 1959 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Number Theory in the Spirit of Ramanujan by : Bruce C. Berndt
Download or read book Number Theory in the Spirit of Ramanujan written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2006 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
Book Synopsis Unsolved Problems in Number Theory by : Richard Guy
Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2004-07-13 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Book Synopsis Primes of the Form x2 + ny2 by : David A. Cox
Download or read book Primes of the Form x2 + ny2 written by David A. Cox and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
Book Synopsis On the Representation of Numbers by Sums of Squares by : Arnold Walfisz
Download or read book On the Representation of Numbers by Sums of Squares written by Arnold Walfisz and published by . This book was released on 1956 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
