Elliptic curves of twin-primes over Gauss field and Diophantine Equations
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Elliptic curves of twin-primes over Gauss field and Diophantine Equations
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| Id. |
20815059 |
| Titulo |
Elliptic curves of twin-primes over Gauss field and Diophantine Equations |
| Autor(es) |
Qiu, DeRong
Zhang, Xianke
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| Localización |
http://arxiv.org/abs/math/0004189
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
Let $p, q$ be twin prime numbers with $q-p=2$ . Consider the elliptic curves
E=E_\sigma: y^2 = x (x+\sigma p)(x+\sigma q) . (\sigma =\pm 1). E=E_\sigma is
also denoted as E_+ or E_- when \sigma = +1or $-1.Here the Mordell-Weil group
and the rank of the elliptic curve E over the Gauss field K=Q(\sqrt -1) (and
over the rational field Q is determined in several cases; and results on
solutions of related Diophantine equations and simultaneous Pellian equations
will be given. The arithmetic constructs over Q of the elliptic curve E have
been studied in the last paper1, the Selmer groups are determined, results on
Mordell-Weil group, rank, Shafarevich-Tate group, and torsion subgroups are
also obtained.
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| Palabras clave |
Mathematics - Number Theory
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| Tipo de recurso |
Texto Narrativo
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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| Requerimientos técnicos |
Browser: Any
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| Fecha de contribución |
26-mar-2007 |
| Contacto |
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