内容

目次

Introduction; Cast of characters; Part I: 1. Congruences and thequotient ring of the integers mod n; 1.2 The discrete Fourier transformon the finite circle; 1.3 Graphs of Z/nZ, adjacency operators,eigenvalues; 1.4 Four questions about Cayley graphs; 1.5 FiniteEuclidean graphs and three questions about their spectra; 1.6 Randomwalks on Cayley graphs; 1.7 Applications in geometry and analysis; 1.8The quadratic reciprocity law; 1.9 The fast Fourier transform; 1.10 TheDFT on finite Abelian groups - finite tori; 1.11 Error-correctingcodes; 1.12 The Poisson sum formula on a finite Abelian group; 1.13Some applications in chemistry and physics; 1.14 The uncertaintyprinciple; Part II. Introduction; 2.1 Fourier transform andrepresentations of finite groups; 2.2 Induced representations; 2.3 Thefinite ax + b group; 2.4 Heisenberg group; 2.5 Finite symmetric spaces- finite upper half planes Hq; 2.6 Special functions on Hq - K-Besseland spherical; 2.7 The general linear group GL(2, Fq); 2.8. Selberg'strace formula and isospectral non-isomorphic graphs; 2.9 The traceformula on finite upper half planes; 2.10 The trace formula for a treeand Ihara's zeta function.