The 3-part of class numbers of quadratic fields

• Autores: Lillian B. Pierce
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 3, 2005, págs. 579-598
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • It is proved that the 3-part of the class number of a quadratic field is in general and if has a divisor of size . These bounds follow as results of nontrivial estimates for the number of solutions to the congruence modulo in the ranges and , where are nonzero integers and is a square-free positive integer. Furthermore, it is shown that the number of elliptic curves over with conductor is in general and if has a divisor of size . These results are the first improvements to the trivial bound and the resulting bound for the 3-part and the number of elliptic curves, respectively.