Publications of the Research Institute for Mathematical Sciences
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Published online: 1997-12-31
On the Thomae Formula for ZN CurvesAtsushi Nakayashiki (1) Kyushu University, Fukuoka, Japan
We shall give an elementary and rigorous proof of the Thomae formula for b>ZN 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 b>ZN invariant 1/2N characteristics.
Nakayashiki Atsushi: On the Thomae Formula for ZN Curves. Publ. Res. Inst. Math. Sci. 33 (1997), 987-1015. doi: 10.2977/prims/1195144885