Counting functions for branched covers of elliptic curves and quasimodular forms
Abstract
We prove that each counting function of the msimple 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.
 Publication:

arXiv eprints
 Pub Date:
 September 1999
 arXiv:
 arXiv:mathph/9909023
 Bibcode:
 1999math.ph...9023O
 Keywords:

 Mathematical Physics;
 Mathematics  Combinatorics;
 Mathematics  Mathematical Physics;
 11F11 (Primary);
 05E05 (Secondary)
 EPrint:
 LaTeX, 16 pages, no figures