Some Applications of Modular Forms
1st Edition
Published on 23. October 2015
978-0-511-89941-6 (ISBN)
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.
Reviews / Votes
Review of the hardback: '... fascinating book ...' Monatshefte fuer MathematikMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 7 Line drawings, unspecified
File size
5,33 MB
ISBN-13
978-0-511-89941-6 (9780511899416)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Peter Sarnak
Some Applications of Modular Forms
Book
07/2008
Cambridge University Press
€60.30
Shipment within 15-20 days
Peter Sarnak
Some Applications of Modular Forms
Book
11/1990
Cambridge University Press
€153.00
Shipment within 15-20 days
Person
Content
Introduction; 1. Modular forms; 2. Invariant means on L?(Sn); 3. Ramanujan graphs; 4. Bounds for Fourier coefficients of 1/2-integral weight; Bibliogrpahy; Index.
