ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11F Pribitkin, Wladimir de Azevedo, Max Planck Institute for Mathematics Bol’s identity, fractional differentiation and automorphic integrals Bol’s identity allows one to map automorphic forms (and also Eichler integrals) of nonpositive integral weight k to automorphic forms of complementary weight 2 − k. We investigate a generalization of Bol’s identity to nonintegral weights. Specifically, we examine the transformation behaviour of functions which result from the fractional differentiation of forms (and integrals) on certain subgroups of SL(2, ℝ) which have arbitrary real weight and multiplier system. We also present an operator which maps forms of any real weight k to forms of weight 2 − k.