MU-THETA FUNCTIONS

WILLIAM GEORGE FREDERICK, Purdue University

Abstract

Let A be an abelian, nilpotent finite dimensional algebra over R. Let B((.),(.)) be a symmetric, bilinear form on A which satisfies B(xy,w) = B(y,xw). Define ((.))--the scalar log function on A by (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) It is shown that the Fourier transform of exp2(pi)i(sigma) (x), for (sigma) a rational member is (sigma)('-n)K((sigma))exp2(pi)i(sigma) ((sigma)('-1)x). That K((sigma)) constant is also the intertwining constant between two theta-like distributions constructed on A. In this paper, we construct (mu)-theta functions, for (sigma) rational, that are equivalent to the (mu)-theta distributions. These functions exhibit properties analogous to the classical theta functions.

Degree

Ph.D.

Subject Area

Mathematics

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