Counting functions for branched covers of elliptic curves and quasi-modular forms

Details Counting functions for branched covers of elliptic curves and quasi-modular forms Counting functions for branched covers of elliptic curves and quasi-modular forms

1999-09-19

arxiv.org/abs/math-ph/9909023v1

Physics

Mathematical Physics

LaTeX, 16 pages, no figures

Scientific paper

We prove that each counting function of the m-simple branched covers with a
fixed genus of an elliptic curve is expressed as a polynomial of the Eisenstein
series E_2, E_4 and E_6 . The special case m=2 is considered by Dijkgraaf.

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