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- Elliptic_unit abstract "In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions, or division values of elliptic functions. They were introduced by Gilles Robert in 1973, and were used by John Coates and Andrew Wiles in their work on the Birch–Swinnerton-Dyer conjecture. Elliptic units are an analogue for imaginary quadratic fields of cyclotomic units. They form an example of an Euler system.A system of elliptic units may be constructed for an elliptic curve E with complex multiplication by the ring of integers R of an imaginary quadratic field F. For simplicity we assume that F has class number one. Let a be an ideal of R with generator α. For a Weierstrass model of E, definewhere Δ is the discriminant and x is the X-coordinate on the Weierstrass model. The function Θ is independent of the choice of model, and is defined over the field of definition of E. Let b be an ideal of R coprime to a and Q an R-generator of the b-torsion. Then Θa(Q) is defined over the ray class field K(b), and if b is not a prime power then Θa(Q) is a global unit: if b is a power of a prime p then Θa(Q) is a unit away from p.The function Θa satisfies a distribution relation for b = (β) coprime to a:".
- Elliptic_unit wikiPageID "5979010".
- Elliptic_unit wikiPageRevisionID "602282179".
- Elliptic_unit hasPhotoCollection Elliptic_unit.
- Elliptic_unit subject Category:Algebraic_number_theory.
- Elliptic_unit subject Category:Modular_forms.
- Elliptic_unit type Abstraction100002137.
- Elliptic_unit type Form106290637.
- Elliptic_unit type LanguageUnit106284225.
- Elliptic_unit type ModularForms.
- Elliptic_unit type Part113809207.
- Elliptic_unit type Relation100031921.
- Elliptic_unit type Word106286395.
- Elliptic_unit comment "In mathematics, elliptic units are certain units of abelian extensions of imaginary quadratic fields constructed using singular values of modular functions, or division values of elliptic functions. They were introduced by Gilles Robert in 1973, and were used by John Coates and Andrew Wiles in their work on the Birch–Swinnerton-Dyer conjecture. Elliptic units are an analogue for imaginary quadratic fields of cyclotomic units.".
- Elliptic_unit label "Elliptic unit".
- Elliptic_unit sameAs m.0fhv3z.
- Elliptic_unit sameAs Q5365804.
- Elliptic_unit sameAs Q5365804.
- Elliptic_unit sameAs Elliptic_unit.
- Elliptic_unit wasDerivedFrom Elliptic_unit?oldid=602282179.
- Elliptic_unit isPrimaryTopicOf Elliptic_unit.