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).
