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ON MAZUR'S CONJECTURE FOR TWISTED L-FUNCTIONS OF ELLIPTIC CURVES OVER TOTALLY REAL OR CM FIELDS

Published online by Cambridge University Press:  25 August 2010

CRISTIAN VIRDOL
CRISTIAN VIRDOL*
Affiliation:
Department of Mathematics, Columbia University, New York, NY 10027, USA e-mail: virdol@math.columbia.edu
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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).

Keywords

11F0311F4111F8011R3711R42
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 207 - 210
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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