Sums of Squares of Integers - Rilegato

Moreno, Carlos J.; Wagstaff, Jr.

Rilegato

ISBN 10: 1584884568 ISBN 13: 9781584884569

Casa editrice: Chapman and Hall/CRC, 2005

Riassunto

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.

Su questo libro

Informazioni sull'autore

Moreno, Carlos J.; Wagstaff, Jr.

Dalla quarta di copertina

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.

Dettagli dell'edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 1584884568
• ISBN 13: 9781584884569
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 366
• Contatto del produttore: Taylor and Francis, GPSR Taylor and Francis; gpsr@taylorandfrancis.com; ; Taylor & Francis Verlag GmbH, Kaufingerstraße 24; München; 80331; Germania