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

Cristian Virdol

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)207-210
Number of pages4
JournalGlasgow Mathematical Journal
Volume53
Issue number1
DOIs
Publication statusPublished - 2011 Jan 1

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CM-field
L-function
Elliptic Curves
Meromorphic
Number field
Argand diagram
Continuation
Functional equation
Finite Set
Entire
Character

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Glasgow Mathematical Journal, Vol. 53, No. 1, 01.01.2011, p. 207-210.

Research output: Contribution to journalArticle

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