Some Applications of Modular Forms

ISBN-13: 9780521402453 / Angielski / Twarda / 1990 / 124 str.

Peter Sarnak; B. Bollobas; W. Fulton

Opis

The theory of modular forms and especially the so-called Ramanujan Conjectures have recently been applied to resolve problems in combinatorics, computer science, analysis, and number theory. Professor Sarnak begins by developing the necessary background material in modular forms. He then considers in detail the solution of three problems: the Rusiewisz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs, e.g. 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.

Recenzje

Review of the hardback: '… fascinating book …' Monatshefte für Mathematik

Spis treści

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.