國立清華大學 數學系

時間: 10:00-11:40, 14:00-14:50 日期: 6/03(三)、6/10(三)、6/16(二)、6/18(四)、6/23(二)、6/25(四)、6/30(二) Abstract: Zeta and L-functions are fundamental topics in number theory, originated from counting integral ideals in a number field and rational points on a variety defined over a finite field. They play pivotal roles in many areas in number theory. Such functions are also defined for compact Riemannian manifolds, counting closed geodesics. They are shown to have links to the spectrum of the Laplacian operator on a manifold although an explicit relation is only known for compact Riemann surfaces which are quotients of the upper half plane. The zeta and L-functions attached to certain finite simplicial complexes have also been studied. They can be explicitly expressed in terms of the combinatorial analogues of the Laplacian operators. In this short course we shall study and compare these functions in different settings. We shall also discuss the famous question of constructing isospectral but non-isometric manifolds in geometry, and rephrase this question in terms of zeta and L-functions.