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

Xavier Guitart*, Marc Masdeu

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)344-361
Number of pages18
JournalExperimental Mathematics
Volume27
Issue number3
DOIs
Publication statusPublished - 3 Jul 2018

Keywords

  • 11F41
  • 11G40
  • 11Y99
  • Modular Abelian varieties
  • p-adic L-invariants
  • p-adic uniformization

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