Sums of Squares of Integers free ebook download.

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Sums of Squares of Integers free ebook download

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Mathematics

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Catalogue

Author(s):	Carlos J. Moreno and Samuel S. Wagstaff Jr.

Date:	2005	Format:	PDF	Language:	English	ISBN/ASIN:	1584884568
Pages:	368	OCR:		Quality:		ISBN13:
Uploader:	Gustavi	Upload Date:	12/13/2019 11:16:41 PM

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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 ting 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.

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2650996	Book	https://novafile.com/0zs9jmzmb0kr...		24.00	Gustavi

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