The Representation of Integers as the Sum of Three Squares PDF Download
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Author: Donald Ian Morrison
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Donald Ian Morrison
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: E. Grosswald
Publisher: Springer Science & Business Media
ISBN: 1461385660
Category : Mathematics
Languages : en
Pages : 262
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Book Description
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.
Author: Carlos J. Moreno
Publisher: CRC Press
ISBN: 1420057235
Category : Computers
Languages : en
Pages : 363
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Book Description
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
Author: Paul Trevier Bateman
Publisher:
ISBN:
Category :
Languages : en
Pages : 118
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Author: Thyrsa Anne Frazier
Publisher:
ISBN:
Category : Integrals
Languages : en
Pages : 78
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Author: C. D. Olds
Publisher: Cambridge University Press
ISBN: 9780883856437
Category : Mathematics
Languages : en
Pages : 198
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A self-contained introduction to the geometry of numbers.
Author: Carlos J. Moreno
Publisher: CRC Press
ISBN: 1584884568
Category : Mathematics
Languages : en
Pages : 368
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Book Description
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.
Author: Manwah Lilian Wong
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Underwood Dudley
Publisher: Courier Corporation
ISBN: 0486134873
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.
Author: Michael David Hirschhorn
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 23
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