TY - JOUR

T1 - On mazur's conjecture for twisted L-functions of elliptic curves over totally real or CM fields

AU - Virdol, Cristian

PY - 2011/1

Y1 - 2011/1

N2 - 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 at s = 1 of L(s, E, ψ), denoted by m(E, ψ) (see Section 2 for the definition).

AB - 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 at s = 1 of L(s, E, ψ), denoted by m(E, ψ) (see Section 2 for the definition).

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U2 - 10.1017/S0017089510000601

DO - 10.1017/S0017089510000601

M3 - Article

AN - SCOPUS:79957471174

VL - 53

SP - 207

EP - 210

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 1

ER -