1. CJM 2001 (vol 53 pp. 434)
 van der Poorten, Alfred J.; Williams, Kenneth S.

Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum
Habib Muzaffar of Carleton University has pointed out to the authors
that in their paper [A] only the result
\[
\pi_{K,d}(x)+\pi_{K^{1},d}(x)=\frac{1}{h(d)}\frac{x}{\log
x}+O_{K,d}\Bigl(\frac {x}{\log^2x}\Bigr)
\]
follows from the prime ideal theorem with remainder for ideal classes,
and not the stronger result
\[
\pi_{K,d}(x)=\frac{1}{2h(d)}\frac{x}{\log
x}+O_{K,d}\Bigl(\frac {x}{\log^2x}\Bigr)
\]
stated in Lemma~5.2. This necessitates changes in Sections~5 and 6 of
[A]. The main results of the paper are not affected by these changes.
It should also be noted that, starting on page 177 of [A], each and
every occurrence of $o(s1)$ should be replaced by $o(1)$.
Sections~5 and 6 of [A] have been rewritten to incorporate the above
mentioned correction and are given below. They should replace the
original Sections~5 and 6 of [A].
Keywords:Dedekind eta function, quadratic irrationalities, binary quadratic forms, form class group Categories:11F20, 11E45 

2. CJM 1999 (vol 51 pp. 176)
 van der Poorten, Alfred; Williams, Kenneth S.

Values of the Dedekind Eta Function at Quadratic Irrationalities
Let $d$ be the discriminant of an imaginary quadratic field. Let
$a$, $b$, $c$ be integers such that
$$
b^2  4ac = d, \quad a > 0, \quad \gcd (a,b,c) = 1.
$$
The value of $\bigl\eta \bigl( (b + \sqrt{d})/2a \bigr) \bigr$ is
determined explicitly, where $\eta(z)$ is Dedekind's eta function
$$
\eta (z) = e^{\pi iz/12} \prod^\ty_{m=1} (1  e^{2\pi imz})
\qquad \bigl( \im(z) > 0 \bigr). %\eqno({\rm im}(z)>0).
$$
Keywords:Dedekind eta function, quadratic irrationalities, binary quadratic forms, form class group Categories:11F20, 11E45 

3. CJM 1998 (vol 50 pp. 1253)
 LópezBautista, Pedro Ricardo; VillaSalvador, Gabriel Daniel

Integral representation of $p$class groups in ${\Bbb Z}_p$extensions and the Jacobian variety
For an arbitrary finite Galois $p$extension $L/K$ of
$\zp$cyclotomic number fields of $\CM$type with Galois group $G =
\Gal(L/K)$ such that the Iwasawa invariants $\mu_K^$, $ \mu_L^$
are zero, we obtain unconditionally and explicitly the Galois
module structure of $\clases$, the minus part of the $p$subgroup
of the class group of $L$. For an arbitrary finite Galois
$p$extension $L/K$ of algebraic function fields of one variable
over an algebraically closed field $k$ of characteristic $p$ as its
exact field of constants with Galois group $G = \Gal(L/K)$ we
obtain unconditionally and explicitly the Galois module structure
of the $p$torsion part of the Jacobian variety $J_L(p)$ associated
to $L/k$.
Keywords:${\Bbb Z}_p$extensions, Iwasawa's theory, class group, integral representation, fields of algebraic functions, Jacobian variety, Galois module structure Categories:11R33, 11R23, 11R58, 14H40 
