By Carlos J. Moreno
Sums of Squares of Integers covers themes in combinatorial quantity thought as they relate to counting representations of integers as sums of a definite variety of squares. The booklet introduces a stimulating quarter of quantity concept the place study keeps to proliferate. it's a booklet of "firsts" - specifically it's the first publication to mix Liouville's user-friendly tools with the analytic equipment of modular features to check the illustration of integers as sums of squares. it's the first ebook to inform tips on how to compute the variety of representations of an integer n because the sum of s squares of integers for any s and n. it's also the 1st booklet to offer an evidence of Szemeredi's theorem, and is the 1st quantity conception ebook to debate how the fashionable thought of modular kinds enhances and clarifies the classical primary effects approximately sums of squares.
The e-book offers numerous present, but nonetheless fascinating and instructive, examples of modular kinds. chapters strengthen invaluable houses of the Bernoulli numbers and illustrate mathematics progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The e-book additionally explains purposes of the speculation to 3 difficulties that lie outdoors of quantity idea within the components of cryptanalysis, microwave radiation, and diamond slicing. The textual content is complemented via the inclusion of over 100 workouts to check the reader's realizing.
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