D.E. Rohrlich, Galois theory, elliptic curves, and root numbers, Compos. Math. 100 (1996), 311--349. Home/Search Document Not in Database Summary Related Articles Check |
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Invariants des courbes de Frey-Hellegouarch et grands groupes de.. - Nitaj (1998) (1 citation) (Correct)
.... Gamma GammaB 2 2 Delta . De meme si E 1 admet en p 3 une r eduction multiplicative, alors p 6 jB p (A p Gamma B p ) et c 6 j B p (mod p) Si la courbe a une r eduction additive en p 3, alors w p = Gamma i Gammaq p j , avec q 2 f1; 2; 3; c 6 g, suivant le symbole de Kodaira (voir [28]) Pour E 1 , si pjB p (A p Gamma B p ) alors le type de Kodaira pour p est de la forme I n et q = 1. Dans le cas o u le signe de l equation fonctionnelle de E 1 (s; t) est 1, on peut calculer la valeur de L(1) a la pr ecision 10 Gammak a l aide de l expression (voir [5] ou [12] ....
D.E. Rohrlich, Galois theory, elliptic curves, and root numbers, Compos. Math. 100 (1996), 311--349.
Modularity Of The Rankin-Selberg L-Series, And Multiplicity.. - Ramakrishnan (Correct)
....When all the # j s are isomorphic, say to #, the root number is W(Sym 2 (#) Sym 2 (#) W(Sym 2 (#) 2 W (1) and this theorem follows in that case from Proposition 6.1 of [PR] Proof. This is an immediate consequence of Proposition 4.3. 1 in conjunction with the method of [PR] see also [Ro]) We give the argument for completeness. It su#ces to show that the local root number at any place v is 1. Clearly, for each j # 4, the associated representation # j,v of W # Fv is self dual with determinant 1 as # j has trivial central character. Put # v = # 1,v# # 2,v# # 3,v# # 4,v ....
: D. Rohrlich, Galois theory, Elliptic curves, and Root numbers, Compositio Mathematica 100, 311-349 (1996).
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