Some Applications of Modular Forms by Peter Sarnak
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Some Applications of Modular Forms
By Peter Sarnak

Some Applications of Modular Forms

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Format: Paperback

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Some Applications of Modular Forms by Peter Sarnak

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. 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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Book Details

ISBN: 9780521067706
ISBN-10: 0521067707
Format: Paperback
(228mm x 152mm x 7mm)
Pages: 124
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 10-Jul-2008
Country of Publication: United Kingdom

Other Editions...


Books By Author Peter Sarnak

Elementary Number Theory, Group Theory and Ramanujan Graphs by Peter Sarnak Elementary Number Theory, Group Theory and Ramanujan Graphs, Hardback (January 2003)

A self-contained treatment of expander graphs which are important in computer science, engineering and mathematics.

Some Applications of Modular Forms by Peter Sarnak Some Applications of Modular Forms, Hardback (November 1990)

An account of unexpected applications of number theory to practical questions that arise in mathematics and computer science.

» View all books by Peter Sarnak

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Recent books by Peter Sarnak close
Elementary Number Theory, Group Theory and Ramanujan Graphs by Peter Sarnak
Elementary Number Theory, Group Theory and Ramanujan Graphs by Peter Sarnak
Some Applications of Modular Forms by Peter Sarnak
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