Geodesic
ON MAZUR'S CONJECTURE FOR TWISTED L-FUNCTIONS OF ELLIPTIC CURVES OVER TOTALLY REAL OR CM FIELDS
Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 207-210

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

Let E be an elliptic curve defined over a number field F, and let Σ be a finite set of finite places of F. Let L(s, E, ψ) be the L-function of E twisted by a finite-order Hecke character ψ of F. It is conjectured that L(s, E, ψ) has a meromorphic continuation to the entire complex plane and satisfies a functional equation s ↔ 2 − s. Then one can define the so called minimal order of vanishing ats = 1 of L(s, E, ψ), denoted by m(E, ψ) (see Section 2 for the definition).
DOI : 10.1017/S0017089510000601
Mots-clés : 11F03, 11F41, 11F80, 11R37, 11R42 
VIRDOL, CRISTIAN. ON MAZUR'S CONJECTURE FOR TWISTED L-FUNCTIONS OF ELLIPTIC CURVES OVER TOTALLY REAL OR CM FIELDS. Glasgow mathematical journal, Tome 53 (2011) no. 1, pp. 207-210. doi: 10.1017/S0017089510000601
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[1] 1.Breuil, C., Conrad, B., Diamond, F. and Taylor, R., On the modularity of elliptic curves over ℚ: Wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), 843–939. Google Scholar | DOI

[2] 2.Langlands, R. P., Base change for GL, Annals of Mathematics Studies, vol. 96 (Hsiang, Wu-chung, Langlands, R. P., Milnor, J. W., Stein, E. M., Editors) (Princeton University Press, Princeton, NJ, 1980). Google Scholar

[3] 3.Mazur, B., Modular curves and arithmetic, in Proceedings of the international congress of mathematicians (Warsaw, Poland, 1983), pp. 185–211. Google Scholar

[4] 4.Rohrlich, D., On L-functions of elliptic curves and cyclotomic towers, Invent. Math. 75 (1984), 404–423. Google Scholar

[5] 5.Rohrlich, D., On L-functions of elliptic curves and anti-cyclotomic towers, Invent. Math. 75 (1984), 383–408. Google Scholar | DOI

[6] 6.Serre, J.-P., Linear representations of finite groups, Graduate Texts in Mathematics, vol. 42 (Springer-Verlag, New York–Heidelberg, 1977). Google Scholar | DOI

[7] 7.Taylor, R., On Galois representations associated to Hilbert modular forms, Invent. Math. 98 (1989), 265–280. Google Scholar | DOI

[8] 8.Virdol, C., On the Birch and Swinnerton–Dyer conjecture for elliptic curves over totally real number fields, Proc. Amer. Math. Soc. 137 (2009), 4019–4024. Google Scholar | DOI

[9] 9.Wiles, A., Modular elliptic curves and Fermat's last theorem, Ann. Math. 141 (1995), 443–551. Google Scholar | DOI

[10] 10.Wintenberger, J. P., Appendix to: On the parity of ranks of Selmer groups IV, Compos. Math. 145 (2009), 1351–1359. Google Scholar

[11] 11.Zhang, S., Elliptic curves, L-functions, and CM-points, in Proceedings for Harvard–MIT joint conference on current development in mathematics (2001), pp. 179–219. Google Scholar

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