Periods of Modular GL2-type Abelian Varieties and p-adic Integration
| Autor: | Xavier Guitart, Marc Masdeu |
|---|---|
| Přispěvatelé: | Universitat de Barcelona |
| Rok vydání: | 2017 |
| Předmět: |
Corbes sobre superfícies
Pure mathematics Ideal (set theory) Mathematics - Number Theory business.industry Corbes el·líptiques General Mathematics 010102 general mathematics 010103 numerical & computational mathematics Type (model theory) Modular design Algebraic number field 11G40 11F41 11Y99 01 natural sciences FOS: Mathematics Elliptic curves Number Theory (math.NT) Curves on surfaces 0101 mathematics Abelian group business Fourier series Mathematics |
| Zdroj: | Dipòsit Digital de la UB Universidad de Barcelona Experimental Mathematics Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a p-adic lattice which is conjectured to be the Tate lattice of an elliptic curve E 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 to f is expected to be, in general, an abelian variety A of dimension d. We also provide numerical evidence supporting the conjectural construction in the case of abelian surfaces. 27 pages. Final version, to appear in Experimental Mathematics |
| Databáze: | OpenAIRE |
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