Some Applications of Modular Forms (Cambridge Tracts in Mathematics, Series Number 99) - Softcover

Sarnak, Peter

Softcover

ISBN 10: 0521067707 ISBN 13: 9780521067706

Publisher: Cambridge University Press, 2008

Synopsis

The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.

About this title

Review

Review of the hardback: '... fascinating book ...' Monatshefte für Mathematik

Book Description

The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2008
• Language: English
• ISBN 10: 0521067707
• ISBN 13: 9780521067706
• Binding: Paperback
• Edition number: 1
• Number of pages: 124