Siegel Modular Forms Having the Same $L$-Functions

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 1, Page 217--227.

Schulze-Pillot, R.
Siegel Modular Forms Having the Same $L$-Functions
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

We show how one can use theta liftings to generate pairs of Siegel modular forms having the same Hecke eigenvalues but different weights. The construction uses the disconnectedness of the orthogonal group. The concrete examples obtained here have arbitrary square free level; although the method works in principle for level one as well we have not yet been able to prove nonvanishing of both forms of a pair in a case of level 1.

Mathematics Subject Classification (1991): Primary 11F46; Secondary 11F27
Mathematical Reviews Number: MR1683309

Received: 1998-04-13