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Some applications of modular forms

Sarnak, Peter.

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Some applications of modular forms

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Some applications of modular forms/ Peter Sarnak.
作者:	Sarnak, Peter.
出版者:	Cambridge :Cambridge University Press, : 1990.,
面頁冊數:	x, 111 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Forms, Modular. -
電子資源:	https://doi.org/10.1017/CBO9780511895593
ISBN:	9780511895593

Some applications of modular forms
Sarnak, Peter.

Some applications of modular forms[electronic resource] /Peter Sarnak. - Cambridge :Cambridge University Press,1990. - x, 111 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;99. - Cambridge tracts in mathematics ;99..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511895593Subjects--Topical Terms:

540521
Forms, Modular.

LC Class. No.: QA243 / .S27 1990

Dewey Class. No.: 512.4

Some applications of modular forms
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520 $a 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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