Abstract
In this work we establish an effective lower bound for the class number of the family of real quadratic fields Q(d), where d=n 2+4 is a square-free positive integer with n=m(m 2-306) for some odd m, with the extra condition (dN)=-1 for N=2 3{dot operator}3 3{dot operator}103{dot operator}10303. This result can be regarded as a corollary of a theorem of Goldfeld and some calculations involving elliptic curves and local heights. The lower bound tending to infinity for a subfamily of the real quadratic fields with discriminant d=n 2+4 could be interesting having in mind that even the class number two problem for these discriminants is not yet solved unconditionally.
Originalsprache | englisch |
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Seiten (von - bis) | 2736-2747 |
Seitenumfang | 12 |
Fachzeitschrift | Journal of Number Theory |
Jahrgang | 132 |
Ausgabenummer | 12 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Dez. 2012 |
Extern publiziert | Ja |
ASJC Scopus subject areas
- Algebra und Zahlentheorie