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

Serdica Mathematical Journal (2009)

- Volume: 35, Issue: 3, page 287-300
- ISSN: 1310-6600

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topMollin, 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 -

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