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Sums of Squares of Integers (Hardcover)
Loot Price: R5,361
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Sums of Squares of Integers (Hardcover)
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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 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.
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