Year: 2013
Type: dissertation
Abstract: Representation theoretic results of Schmidt suggest that one should be able to construct a Saito-Kurokawa lifting that has mixed level, i.e., the level is paramodular at some places and congruence level at other places.Adapting Schmidt's proof we show that indeed one can construct such a lifting using representation theory.The goal then becomes to construct such a lifting classically as the more explicit nature of such a construction lends itself nicely to arithmetic applications.To this end we obtain half of the classical construction by giving the cuspidal lifting G M : J c κ,t (Γ 0 (M )) → S κ (Γ M [t]), generalizing the cuspidal lifting of Ibukiyama and the cuspidal lifting of Gritsenko.
Source: TigerPrints (Clemson University)
Author: Dania Zantout
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W228710968