On the Thomae Formula for Curves

  • Atsushi Nakayashiki

    Kyushu University, Fukuoka, Japan


We shall give an elementary and rigorous proof of the Thomae formula for curves which was discovered by Bershadsky and Radul [1, 2]. Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szego kernels and prove the vanishing of zero values of derivatives of theta functions with invariant characteristics.

Cite this article

Atsushi Nakayashiki, On the Thomae Formula for Curves. Publ. Res. Inst. Math. Sci. 33 (1997), no. 6, pp. 987–1015

DOI 10.2977/PRIMS/1195144885