A note on automorphic forms of weight one and weight three Academic Article uri icon


  • In this paper the author develops an interesting relationship between classical automorphic forms of weights one and three, and the solutions of certain second order differential equations related to elliptic (modular) surfaces. In particular for a cusp form of weight three, it is shown that the special values of the associated Dirichlet series can be determined from the periods of an inhomogeneous differential equation, or what is the same thing, the monodromy of an associated third order differential equation. Explicit examples are provided for principal congruence subgroups ( N ) Gamma (N) with N 0 mod 4 N equiv 0,operatorname {mod} ,4 .

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • Stiller, P. F.

citation count

  • 4

complete list of authors

  • Stiller, Peter F

publication date

  • January 1985