Empirically determined Apéry-like formulae for .
We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra . The Tate conjecture predicts that is the full endomorphism algebra of the motive. We also investigate the Brauer class of . For example we show that if the nebentypus is real and is a prime that does not divide the level, then the local behaviour of at a place lying above is essentially determined...
Cet article traite des endomorphismes de l’algèbre de Hadamard des suites et plus particulièrement de l’algèbre des suites récurrentes linéaires. Il caractérise les endomorphismes continus de l’algèbre des suites et contient, dans le cas d’un corps commutatif de caractéristique nulle, une détermination complète des endomorphismes continus de l’algèbre des suites récurrentes linéaires grâce à la notion nouvelle d’application semi-affine de dans .
We show that for a fixed integer n ≠ ±2, the congruence x² + nx ± 1 ≡ 0 (mod α) has the solution β with 0 < β < α if and only if α/β has a continued fraction expansion with sequence of quotients having one of a finite number of possible asymmetry types. This generalizes the old theorem that a rational number α/β > 1 in lowest terms has a symmetric continued fraction precisely when β² ≡ ±1(mod α ).