ar X iv :1 30 7. 39 19 v1 [ ma th. DG ] 15 Ju l 2 01 3 EIGENVALUES OF LAPLACIAN AND MULTI-WAY ISOPERIMETRIC CONSTANTS ON WEIGHTED RIEMANNIAN MANIFOLDS KEI FUNANO Abstract.…
Lecture 4. Proof of Ihara’s Theorem, Edge Zetas, Quantum Chaos Ihara’s Theorem. A=adjacency matrix, Q +I = diagonal matrix of degrees, r=rank fundamental group. Ihara…