1. CMB 2011 (vol 55 pp. 774)
 Mollin, R. A.; Srinivasan, A.

Pell Equations: NonPrincipal Lagrange Criteria and Central Norms
We provide a criterion for the central norm to be
any value in the simple continued fraction expansion of $\sqrt{D}$
for any nonsquare integer $D>1$. We also provide a simple criterion
for the solvability of the Pell equation $x^2Dy^2=1$ in terms of
congruence conditions modulo $D$.
Keywords:Pell's equation, continued fractions, central norms Categories:11D09, 11A55, 11R11, 11R29 

2. CMB 2011 (vol 54 pp. 330)
 Mouhib, A.

Sur la borne infÃ©rieure du rang du 2groupe de classes de certains corps multiquadratiques
Soient $p_1,p_2,p_3$ et $q$ des nombres premiers distincts tels que
$p_1\equiv p_2\equiv p_3\equiv q\equiv 1 \pmod{4}$, $k = \mathbf{Q}
(\sqrt{p_1}, \sqrt{p_2}, \sqrt{p_3}, \sqrt{q})$ et $\operatorname{Cl}_2(k)$ le
$2$groupe de classes de $k$. A. FrÃ¶hlich a
dÃ©montrÃ© que $\operatorname{Cl}_2(k)$ n'est jamais trivial. Dans cet article,
nous donnons une extension de ce rÃ©sultat, en dÃ©montrant que le
rang de $\operatorname{Cl}_2(k)$ est toujours supÃ©rieur ou Ã©gal Ã $2$. Nous
dÃ©montrons aussi, que la valeur $2$ est optimale pour une famille
infinie de corps $k$.
Keywords:class group, units, multiquadratic number fields Categories:11R29, 11R11 

3. CMB 2007 (vol 50 pp. 409)
4. CMB 2005 (vol 48 pp. 121)
5. CMB 2004 (vol 47 pp. 431)
 Osburn, Robert

A Note on $4$Rank Densities
For certain real quadratic number fields, we prove density results concerning
$4$ranks of tame kernels. We also discuss a relationship between $4$ranks of
tame kernels and %% $4$class ranks of narrow ideal class groups. Additionally,
we give a product formula for a local Hilbert symbol.
Categories:11R70, 19F99, 11R11, 11R45 

6. CMB 2003 (vol 46 pp. 39)
 Bülow, Tommy

Power Residue Criteria for Quadratic Units and the Negative Pell Equation
Let $d>1$ be a squarefree integer. Power residue criteria for the
fundamental unit $\varepsilon_d$ of the real quadratic fields $\QQ
(\sqrt{d})$ modulo a prime $p$ (for certain $d$ and $p$) are proved by
means of class field theory. These results will then be interpreted
as criteria for the solvability of the negative Pell equation $x^2 
dp^2 y^2 = 1$. The most important solvability criterion deals with
all $d$ for which $\QQ (\sqrt{d})$ has an elementary abelian 2class
group and $p\equiv 5\pmod{8}$ or $p\equiv 9\pmod{16}$.
Categories:11R11, 11R27 

7. CMB 2002 (vol 45 pp. 428)
 Mollin, R. A.

Criteria for Simultaneous Solutions of $X^2  DY^2 = c$ and $x^2  Dy^2 = c$
The purpose of this article is to provide criteria for the
simultaneous solvability of the Diophantine equations $X^2  DY^2 =
c$ and $x^2  Dy^2 = c$ when $c \in \mathbb{Z}$, and $D \in
\mathbb{N}$ is not a perfect square. This continues work in
\cite{me}\cite{alfnme}.
Keywords:continued fractions, Diophantine equations, fundamental units, simultaneous solutions Categories:11A55, 11R11, 11D09 

8. CMB 2000 (vol 43 pp. 218)
9. CMB 1998 (vol 41 pp. 328)
 Mollin, R. A.

Class number one and primeproducing quadratic polynomials revisited
Over a decade ago, this author produced class number one criteria for
real quadratic fields in terms of primeproducing quadratic
polynomials. The purpose of this article is to revisit the problem
from a new perspective with new criteria. We look at the more general
situation involving arbitrary real quadratic orders rather than the
more restrictive field case, and use the interplay between the various
orders to provide not only more general results, but also simpler proofs.
Categories:11R11, 11R09, 11R29 

10. CMB 1997 (vol 40 pp. 214)
 Mollin, R. A.; Goddard, B.; Coupland, S.

Polynomials of quadratic type producing strings of primes
The primary purpose of this paper is to provide necessary and
sufficient conditions for certain quadratic polynomials of negative
discriminant (which we call EulerRabinowitsch type), to produce
consecutive prime values for an initial range of input values less than
a Minkowski bound. This not only generalizes the classical work of
Frobenius, the later developments by Hendy, and the generalizations by
others, but also concludes the line of reasoning by providing a
complete list of all such primeproducing polynomials, under the
assumption of the generalized Riemann hypothesis ($\GRH$). We demonstrate
how this primeproduction phenomenon is related to the exponent of the
class group of the underlying complex quadratic field. Numerous
examples, and a remaining conjecture, are also given.
Categories:11R11, 11R09, 11R29 
