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Title: Class Number Two for Real Quadratic Fields of Richaud-Degert Type
Authors: Mollin, R. A.
Keywords: Quadratic Fields
Prime-Producing Polynomials
Class Numbers
Continued Fractions
Cycles of Ideals
Richaud-Degert Types
Issue Date: 2009
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 3, (2009), 287p-300p
Abstract: This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination of the class number 2 problem for such types. For some values the determination is unconditional, and for others, the wide Richaud-Degert types, the determination is conditional on the generalized Riemann hypothesis (GRH).
Description: 2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.
ISSN: 1310-6600
Appears in Collections:Volume 35, Number 3

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