### Abstract

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).

Original language | English |
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Pages (from-to) | 207-210 |

Number of pages | 4 |

Journal | Glasgow Mathematical Journal |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*Glasgow Mathematical Journal*, vol. 53, no. 1, pp. 207-210. https://doi.org/10.1017/S0017089510000601

**On mazur's conjecture for twisted L-functions of elliptic curves over totally real or CM fields.** / Virdol, Cristian.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Virdol, Cristian

PY - 2011/1/1

Y1 - 2011/1/1

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).

UR - http://www.scopus.com/inward/record.url?scp=79957471174&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957471174&partnerID=8YFLogxK

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 -