Some Applications of Modular Forms

Language: English

Published by Cambridge University Press, GB, 2008

0521067707 / 9780521067706

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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.

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Title
Some Applications of Modular Forms
Author
Peter Sarnak
Publisher
Cambridge University Press, GB
Publication year
2008
Condition
New
Binding
Paperback
Language
English
ISBN 10
0521067707
ISBN 13
9780521067706
Item weight
190 grams

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