Some applications of modular forms
著者
書誌事項
Some applications of modular forms
（Cambridge tracts in mathematics, 99）
Cambridge University Press, 2008, c1990
- : pbk
大学図書館所蔵 全4件
注記
Originally published: 1990
"Digitally printed version 2008"--T.p. verso
"Paperback Re-issue"--Back cover
Includes bibliographical references (p. 103-109) and index
内容説明・目次
内容説明
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.
目次
- 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.
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