Hershel Farkas

Affiliation: The Hebrew University of Jerusalem

Email: farkas@math.huji.ac.il

Title Of Talk: Generalizations of Hutchinson's Curve and the Thomae Formula

Abstract: In this note we consider the one dimensional family of compact Riemann surfaces satisfying the algebraic equation $$ W^n = (z-\lambda_0)(z-lambda_1)(z-\lambda)^{n-1}. $$ This is a family of hyperelliptic surfaces of genus $ g = n-1 $. Hutchinson considered the case of n=3. We shall show how the theta functions associated with this family satisfy analogues of Jacobi's formula for elliptic curves. While in Jacobi's case the theta functions were the classical ones with integer characteristic, here we will obtain theta functions with rational characteristic. Alternatively our formulas can be thought of as Thomae formulae for what is referred to as singular $Z_n$ curves.

Last update made Mon Mar 3 16:12:45 EST 2008.
Please report problems to: frank@math.ufl.edu