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Title: Periods of Modular GL2-type Abelian Varieties and p-adic Integration
Author: Guitart Morales, Xavier
Masdeu, Marc
Keywords: Corbes el·líptiques
Corbes sobre superfícies
Elliptic curves
Curves on surfaces
Issue Date: 1-Mar-2017
Publisher: Taylor and Francis
Abstract: Let F be a number field and an integral ideal. Let f be a modular newform over F of level with rational Fourier coefficients. Under certain additional conditions, Guitart and colleagues [Guitart et al. 16[Guitart et al. 16] X. Guitart, M. Masdeu, and M. Haluk Şengün. "Uniformization of Modular Elliptic Curves via p-adic Periods." J. Algebra 445 (2016), 458-502. MR 3418066 [Crossref], [Web of Science ®] , [Google Scholar] ] 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.
Note: Versió postprint del document publicat a:
It is part of: Experimental Mathematics, 2017, vol. 27, num. 3, p. 344-361
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ISSN: 1058-6458
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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