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

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DOI

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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