Geodesic
Two Modularity Lifting Conjectures for Families of Siegel Modular Forms
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 565-574

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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. 
@article{MZM_2010_88_4_a7,
     author = {A. A. Panchishkin},
     title = {Two {Modularity} {Lifting} {Conjectures} for {Families} of {Siegel} {Modular} {Forms}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--574},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a7/}
}
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A. A. Panchishkin. Two Modularity Lifting Conjectures for Families of Siegel Modular Forms. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 565-574. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a7/