235 research outputs found
The weight reduction of mod Siegel modular forms for
In this paper we investigate the (classical) weights of mod Siegel
modular forms of degree 2 toward studying Serre's conjecture for . We
first construct various theta operators on the space of such forms a la Katz
and define the theta cycles for the specific theta operators. Secondly we study
the partial Hasse invariants on each Ekedahl-Oort strata and their local
behaviors. This enable us to obtain a kind of weight reduction theorem for mod
Siegel modular forms of degree 2 without increasing level.Comment: This is an extended version of my previous article entitled as "The
weight in Serre's conjecture for ". Lots of revisions have mad
On the class numbers of the fields of the -torsion points of elliptic curves over
Let be an elliptic curve over which has multiplicative
reduction at a fixed prime . For each positive integer we put
. The aim of this paper is to extend the author's
previous our results concerning with the order of the -Sylow group of the
ideal class group of to more general setting. We also modify the previous
lower bound of the order and describe the new lower bound in terms of the
Mordell-Weil rank of and the ramification related to .Comment: 16 pages. We refined the main theore
An explicit computation of p-stabilized vectors
In this paper, we give a method to compute p-stabilized vectors in the space
of parahori-fixed vectors for connected reductive groups over p-adic fields.
The application to the global setting is also discussed. In particular, we give
an explicit p-stabilized form of a Saito-Kurokawa lift.Comment: 21 page
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