Petersburg Department of Steklov Institute of Mathematics

PREPRINT 16/1999

RELATIONSHIP BETWEEN THE SPECTRAL THEORIES OF AUTOMORPHIC FUNCTIONS OF WEIGHT 0 AND 1/2

This preprint was accepted September 15, 1998
Contact: V. A. Bykovskii

ABSTRACT:
In the present paper, it is established a spectral expansion of
the convolution of an Eisenstein series of weight zero and the
classical Jacobi theta function with a nontrivial shift in
eigenfunctions of the space of automorphic functions of weight
zero, invariant relative to the group $SL(2,\Bbb Z)$.