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

Hiroyuki Ochiai

Published 1999-09-19Version 1

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.