On generalized gauss-hecke sums and theta constants

Abstract

In the quadratic case, the analytic proof of the reciprocity law for a numbr field involves a connection between Gauss-Hecke sums and theta constants or Thetanullwerte. We propose a generalization of Gauss-Hecke sums to higher degrees and discuss some aspects of the problem of determining higher transcendental functions by suitable boundary conditions which involve these objects in a natural way.

Keywords:

• Gauss-Hecke sums
• Theta-functions

MSC(1991):

• 11F25
• 11F27
• 11L15
• 11R04
• 14H42