Periods of Modular GL2-type Abelian Varieties and p-adic Integration

Xavier Guitart*, Marc Masdeu

*Autor corresponent d’aquest treball

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Resum

Let F be a number field and (Formula presented.) an integral ideal. Let f be a modular newform over F of level (Formula presented.) with rational Fourier coefficients. Under certain additional conditions, Guitart and colleagues [Guitart et al. 16] constructed a p-adic lattice which is conjectured to be the Tate lattice of an elliptic curve Ef whose L-function equals that of f. The aim of this note is to generalize this construction when the Hecke eigenvalues of f generate a number field of degree d ⩾ 1, in which case the geometric object associated with f is expected to be, in general, an abelian variety Af of dimension d. We also provide numerical evidence supporting the conjectural construction in the case of abelian surfaces.

Idioma originalAnglès
Pàgines (de-a)344-361
Nombre de pàgines18
RevistaExperimental Mathematics
Volum27
Número3
DOIs
Estat de la publicacióPublicada - 3 de jul. 2018

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