Mathematical Sciences: Conference on Zeta Functions in Number Theory and Geometric Analysis

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Zeta functions play a well-recognized role in many areas of mathematics. In 1992-93, the Japan-US Mathematical Institute at Johns Hopkins University is hosting a special year on zeta functions in number theory and in geometric analysis. This award is for a conference to be held March 29- April 3,1993, to bring together researchers in these subjects. Visitors to Hopkins during Spring 1993 in areas related to number theoretic zeta functions include A. Gyoja, T. Kimura, D. Meuser, F. Sato, and T. Yano. Visitors in areas related to the geometric analysis aspects include T. Adachi, A. Katsuda, Y. Petridis, and T. Sunada. One connection between these two areas is the study of zeta functions associated to quotients of symmetric spaces, e.g. in the spectral theory of automorphic forms. Another is the study of the fine structure of the zeroes of various L-functions, which resembles that of the eigen-values of various Laplacians. A more informal connections is that the principal researchers in these areas often have an intense interest in the strong analogies between their work and that in areas not directly related. We will describe the two areas separately below, but in the second part (zeta functions in geometric analysis) we will try to indicate some of the overlap between number-theoretic and geometric-analytic zeta functions. This project proposes a conference on zeta functions in number theory and geometric analysis, with emphasis on the following subjects: (i) zeta functions of prehomogeneous vector spaces and Igusa zeta functions; (ii) the zeta functions which arise in the spectral theory of the Laplacian. The proposed conference is planned so as to take advantage of the concentration of experts in these areas present at Johns Hopkins in connection with the concentration year held by the Japan-U.S. Mathematical Institute.