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

ζ函数在数学的许多领域发挥着公认的作用。1992- 1993年，约翰霍普金斯大学的日美数学研究所将举办一个关于数论和几何分析中的ζ函数的特别年。这一奖项将颁发给将于1993年3月29日至4月3日举行的一次会议，该会议将召集这些学科的研究人员。1993年春季访问霍普金斯大学数论ζ函数相关领域的访客包括A. Gyoja， T. Kimura， D. Meuser， F. Sato和T. Yano。与几何分析相关领域的参观者包括T. Adachi， A. Katsuda， Y. Petridis和T. Sunada。这两个领域之间的一个联系是研究与对称空间商相关的ζ函数，例如在自同构形式的谱理论中。另一个是研究各种l函数的零点的精细结构，它类似于研究各种拉普拉斯算子的特征值。更非正式的联系是，这些领域的主要研究人员通常对他们的工作与不直接相关的领域的工作之间的强烈类比有着浓厚的兴趣。我们将在下面分别描述这两个领域，但在第二部分（几何分析中的zeta函数）中，我们将尝试指出数论和几何解析zeta函数之间的一些重叠。本项目拟召开数论与几何分析中的zeta函数会议，重点讨论以下问题：(1)预齐次向量空间中的zeta函数和Igusa zeta函数；（二）拉普拉斯谱理论中出现的ζ函数。这次会议的目的是利用约翰霍普金斯大学在这些领域的专家集中的机会，与日美同盟举行的集中年相结合。数学研究所。

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.