@article{e90e30cae4df4ca8a65211a2322c085b,
title = "Periods of Modular GL2-type Abelian Varieties and p-adic Integration",
abstract = "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.",
keywords = "11F41, 11G40, 11Y99, Modular Abelian varieties, p-adic L-invariants, p-adic uniformization",
author = "Xavier Guitart and Marc Masdeu",
note = "Funding Information: Xavier Guitart was supported by MTM2015-66716-P and MTM2015-63829, and Marc Masdeu was supported by MSC– IF–H2020–ExplicitDarmonProg. This project has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation program (grant agreement no. 682152). Funding Information: We wish to thank Lassina Dembele, Ariel Pacetti, Haluk Sengun, John Voight, and Xavier Xarles for feedback and helpful conversations during this project. Marc Masdeu thanks the Number Theory group of the University of Warwick for providing an outstanding working environment, and Xavier Guitart is thankful to the Essen Seminar for Algebraic Geometry and Arithmetic for their hospitality during his stay. Xavier Guitart was supported by MTM2015-66716-P and MTM2015-63829, and Marc Masdeu was supported by MSC?IF?H2020?ExplicitDarmonProg. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 682152). Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Taylor & Francis.",
year = "2018",
month = jul,
day = "3",
doi = "10.1080/10586458.2017.1284624",
language = "English",
volume = "27",
pages = "344--361",
journal = "Experimental Mathematics",
issn = "1058-6458",
publisher = "Taylor and Francis Ltd.",
number = "3",
}