1. CMB Online first
 Dobrowolski, Edward

A note on Lawton's theorem
We prove Lawton's conjecture about the upper bound on the measure
of the set on the unit circle on which a complex polynomial with
a bounded number of coefficients takes small values. Namely,
we prove that Lawton's bound holds for polynomials that are not
necessarily monic. We also provide an analogous bound for polynomials
in several variables. Finally, we investigate the dependence
of the bound on the multiplicity of zeros for polynomials in
one variable.
Keywords:polynomial, Mahler measure Categories:11R09, 11R06 

2. CMB 2012 (vol 56 pp. 759)
 Issa, Zahraa; Lalín, Matilde

A Generalization of a Theorem of Boyd and Lawton
The Mahler measure of a nonzero $n$variable polynomial $P$ is the integral of
$\logP$ on the unit $n$torus. A result of Boyd and Lawton says that
the Mahler measure of a multivariate polynomial is the limit of Mahler
measures of univariate polynomials. We prove the analogous
result for different extensions of Mahler measure such as generalized
Mahler measure (integrating the maximum of $\logP$ for possibly
different $P$'s),
multiple Mahler measure (involving products of $\logP$ for possibly
different $P$'s), and higher Mahler measure (involving $\log^kP$).
Keywords:Mahler measure, polynomial Categories:11R06, 11R09 

3. CMB 2011 (vol 55 pp. 26)
 Bertin, Marie José

A Mahler Measure of a $K3$ Surface Expressed as a Dirichlet $L$Series
We present another example of a $3$variable polynomial defining a $K3$hypersurface
and having a logarithmic Mahler measure expressed in terms of a Dirichlet
$L$series.
Keywords:modular Mahler measure, EisensteinKronecker series, $L$series of $K3$surfaces, $l$adic representations, LivnÃ© criterion, RankinCohen brackets Categories:11, 14D, 14J 

4. CMB 2011 (vol 54 pp. 739)
 Samuels, Charles L.

The Infimum in the Metric Mahler Measure
Dubickas and Smyth defined the metric Mahler measure on the
multiplicative group of nonzero algebraic numbers.
The definition involves taking an infimum over representations
of an algebraic number $\alpha$ by other
algebraic numbers. We verify their conjecture that the
infimum in its definition is always achieved, and we establish its
analog for the ultrametric Mahler measure.
Keywords:Weil height, Mahler measure, metric Mahler measure, Lehmer's problem Categories:11R04, 11R09 

5. CMB 2007 (vol 50 pp. 191)
 Drungilas, Paulius; Dubickas, Artūras

Every Real Algebraic Integer Is a Difference of Two Mahler Measures
We prove that every real
algebraic integer $\alpha$ is expressible by a
difference of two Mahler measures of integer polynomials.
Moreover, these polynomials can be chosen in such a way that they
both have the same degree as that of $\alpha$, say
$d$, one of these two polynomials is irreducible and
another has an irreducible factor of degree $d$, so
that $\alpha=M(P)bM(Q)$ with irreducible polynomials
$P, Q\in \mathbb Z[X]$ of degree $d$ and a
positive integer $b$. Finally, if $d \leqslant 3$, then one can take $b=1$.
Keywords:Mahler measures, Pisot numbers, Pell equation, $abc$conjecture Categories:11R04, 11R06, 11R09, 11R33, 11D09 

6. CMB 2002 (vol 45 pp. 231)
 Hironaka, Eriko

Erratum:~~The Lehmer Polynomial and Pretzel Links
Erratum to {\it The Lehmer Polynomial and Pretzel Links},
Canad. J. Math. {\bf 44}(2001), 440451.
Keywords:Alexander polynomial, pretzel knot, Mahler measure, Salem number, Coxeter groups Categories:57M05, 57M25, 11R04, 11R27 

7. CMB 2002 (vol 45 pp. 196)
 Dubickas, Artūras

Mahler Measures Close to an Integer
We prove that the Mahler measure of an algebraic number cannot be too
close to an integer, unless we have equality. The examples of certain
Pisot numbers show that the respective inequality is sharp up to a
constant. All cases when the measure is equal to the integer are
described in terms of the minimal polynomials.
Keywords:Mahler measure, PV numbers, Salem numbers Categories:11R04, 11R06, 11R09, 11J68 

8. CMB 2001 (vol 44 pp. 440)
 Hironaka, Eriko

The Lehmer Polynomial and Pretzel Links
In this paper we find a formula for the Alexander polynomial
$\Delta_{p_1,\dots,p_k} (x)$ of pretzel knots and links with
$(p_1,\dots,p_k, \nega 1)$ twists, where $k$ is odd and
$p_1,\dots,p_k$ are positive integers. The polynomial $\Delta_{2,3,7}
(x)$ is the wellknown Lehmer polynomial, which is conjectured to have
the smallest Mahler measure among all monic integer polynomials. We
confirm that $\Delta_{2,3,7} (x)$ has the smallest Mahler measure among
the polynomials arising as $\Delta_{p_1,\dots,p_k} (x)$.
Keywords:Alexander polynomial, pretzel knot, Mahler measure, Salem number, Coxeter groups Categories:57M05, 57M25, 11R04, 11R27 
