Sums of Squares of Integers

Carlos J. Moreno, Samuel S. Wagstaff Jr.

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English

Chapman & Hall/CRC
05 September 2019

Discrete mathematics; Number theory; Combinatorics & graph theory; Automatic control engineering; Environmental science, engineering & technology

"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."

By: Carlos J. Moreno, Samuel S. Wagstaff Jr.
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 539g
ISBN: 9780367391614
ISBN 10: 0367391619
Pages: 368
Publication Date: 05 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction. Elementary Methods. Bernoulli Numbers. Examples of Modular Forms. Hecke's Theory of Modular Forms. Representation of Numbers as Sums of Squares. Arithmetic Progressions. Applications. References. Index.

Moreno, Carlos J.; Wagstaff, Jr.