Geodesic
Twisted Hasse-Weil L-Functions and the Rank of Mordell-Weil Groups
Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 749-771

Voir la notice de l'article provenant de la source Cambridge University Press

Following a method outlined by Greenberg, root number computations give a conjectural lower bound for the ranks of certain Mordell–Weil groups of elliptic curves. More specifically, for PQn a PGL2(Z/p n Z)–extension of Q and E an elliptic curve over Q, define the motive E⊗ ρ, where ρ is any irreducible representation of Gal(PQ n /Q). Under some restrictions, the root number in the conjectural functional equation for the L-function of E ⊗ ρ is easily computable, and a ‘–1’ implies, by the Birch and Swinnerton–Dyer conjecture, that ρ is found in E(PQn ) ⊗ C. Summing the dimensions of such ρ gives a conjectural lower bound ofp2n–p2n–1–p–1for the rank of E(PQn ).
DOI : 10.4153/CJM-1997-037-7
Mots-clés : 11G05, 14G10 
Twisted Hasse-Weil L-Functions and the Rank of Mordell-Weil Groups. Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 749-771. doi: 10.4153/CJM-1997-037-7
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