This article is cited in 1 paper

Two Modularity Lifting Conjectures for Families of Siegel Modular Forms

A. A. Panchishkin

Institut Fourier, Universit\'е Grenoble-1

Abstract: For a prime $p$ and a positive integer $n$, using certain lifting procedures, we study some constructions of $p$-adic families of Siegel modular forms of genus $n$. Describing $L$-functions attached to Siegel modular forms and their analytic properties, we formulate two conjectures on the existence of the modularity liftings from $\operatorname{GSp}_{r}\times \operatorname{GSp}_{2m}$ to $\operatorname{GSp}_{r+2m}$ for some positive integers $r$ and $m$.

Keywords: $p$-adic families, Siegel modular forms, Hecke operators, Siegel–Eisenstein series, Ikeda–Miyawaki lift.

UDC: 511.333

Received: 30.11.2009

DOI: 10.4213/mzm8853

 English version: Mathematical Notes, 2010, 88:4, 544–551

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