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Sums of Squares of Integers (Discrete Mathematics and Its Applications) - Tapa dura

Moreno, Carlos J.; Wagstaff, Jr.

 
9781584884569: Sums of Squares of Integers (Discrete Mathematics and Its Applications)
Tapa dura
ISBN 10: 1584884568 ISBN 13: 9781584884569
Editorial: Chapman and Hall/CRC, 2005

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Moreno, Carlos J.; Wagstaff, Jr.

De la contraportada

Sums of Squares of Integers is the first book to combine elementary methods with analytic methods of modular functions to study the representation of integers as sums of squares. It is the first to explain how to compute the number of representations of an integer n as the sum of s squares for any s and n. It is also the first to give a proof of Szemeredi's theorem, an important theorem in modern number theory, and it discusses how the modern theory of modular forms complements and clarifies the classical, fundamental results about sums of squares. The text includes applications to fields such as cryptography, crystallography, and thermal radiation.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Chapman and Hall/CRC
Año de publicación
2005
Idioma
Inglés
ISBN 10 
1584884568
ISBN 13 
9781584884569
Encuadernación
Tapa dura
Número de edición
1
Número de páginas
366
Contacto del fabricante
Taylor and Francis, GPSR Taylor and Francis
gpsr@taylorandfrancis.com

Taylor & Francis Verlag GmbH, Kaufingerstraße 24
München
80331
Alemania