Class Number Two for Real Quadratic Fields of Richaud-Degert Type

Mollin, R. A.. "Class Number Two for Real Quadratic Fields of Richaud-Degert Type." Serdica Mathematical Journal 35.3 (2009): 287-300. <http://eudml.org/doc/281458>.

@article{Mollin2009,
abstract = {2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.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).},
author = {Mollin, R. A.},
journal = {Serdica Mathematical Journal},
keywords = {Quadratic Fields; Prime-Producing Polynomials; Class Numbers; Continued Fractions; Cycles of Ideals; Richaud-Degert Types; Quadratic fields; prime producing polynomials; class numbers; continued fractions; cycles of ideals; Richaud-Degert type.},
language = {eng},
number = {3},
pages = {287-300},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Class Number Two for Real Quadratic Fields of Richaud-Degert Type},
url = {http://eudml.org/doc/281458},
volume = {35},
year = {2009},
}

TY - JOUR
AU - Mollin, R. A.
TI - Class Number Two for Real Quadratic Fields of Richaud-Degert Type
JO - Serdica Mathematical Journal
PY - 2009
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 3
SP - 287
EP - 300
AB - 2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.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).
LA - eng
KW - Quadratic Fields; Prime-Producing Polynomials; Class Numbers; Continued Fractions; Cycles of Ideals; Richaud-Degert Types; Quadratic fields; prime producing polynomials; class numbers; continued fractions; cycles of ideals; Richaud-Degert type.
UR - http://eudml.org/doc/281458
ER -