Class Number Two for Real Quadratic Fields of Richaud-Degert Type
Serdica Mathematical Journal, Tome 35 (2009) no. 3, pp. 287-300
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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).
Keywords:
Quadratic Fields, Prime-Producing Polynomials, Class Numbers, Continued Fractions, Cycles of Ideals, Richaud-Degert Types
@article{SMJ2_2009_35_3_a3,
author = {Mollin, R. A.},
title = {Class {Number} {Two} for {Real} {Quadratic} {Fields} of {Richaud-Degert} {Type}},
journal = {Serdica Mathematical Journal},
pages = {287--300},
publisher = {mathdoc},
volume = {35},
number = {3},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_2009_35_3_a3/}
}
Mollin, R. A. Class Number Two for Real Quadratic Fields of Richaud-Degert Type. Serdica Mathematical Journal, Tome 35 (2009) no. 3, pp. 287-300. http://geodesic.mathdoc.fr/item/SMJ2_2009_35_3_a3/