Mathematical Sciences: Harmonic Analysis on Symmetric and Locally Symmetric Spaces

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9401193 STANTON Stanton will continue his work on holomorphic torsion, extending it to the doubly-laced case. He will attempt to show that the formal geometric zeta function has a meromorphic extension to the complex plane. He will examine a number of other cases of locally symmetric or locally homogeneous geometries to test a conjectured technique for constructing geometric zeta functions using compactifications of the simply connected covering space. The general area of the research is analysis on symmetric spaces. One is interested in finding analogues of the classical special functions defined on geometric spaces that are generalizations of classical domains in n-dimensional complex space. ***