Thetanulls and differential equations

@inproceedings{Zudilin2001ThetanullsAD,
  title={Thetanulls and differential equations},
  author={V. V. Zudilin},
  year={2001}
}
  • V. V. Zudilin
  • Published 2001
The closedness of the system of thetanulls (and the Siegel modular forms) and their first derivatives with respect to differentiation is well-known in the one-dimensional case. It is shown in the present paper that thetanulls and their various logarithmic derivatives satisfy a non-linear system of differential equations; only one and two-dimensional versions of this result were known before. Several distinct examples of such systems are presented, and a theorem on the transcendence degree of… CONTINUE READING