## Experimental Mathematics

- Experiment. Math.
- Volume 14, Issue 4 (2005), 403-414.

### Small Limit Points of Mahler's Measure

David W. Boyd and Michael J. Mossinghoff

#### Abstract

Let $M(P(z_1,\dots,z_n))$ denote Mahler's measure of the polynomial $P(z_1,\dots,z_n)$. Measures of polynomials in $n$ variables arise naturally as limiting values of measures of polynomials in fewer variables. We describe several methods for searching for polynomials in two variables with integer coefficients having small measure, demonstrate effective methods for computing these measures, and identify 48 polynomials $P(x,y)$ with integer coefficients, irreducible over $\Rats$, for which $1 < M(P(x,y)) < 1.37$.

#### Article information

**Source**

Experiment. Math., Volume 14, Issue 4 (2005), 403-414.

**Dates**

First available in Project Euclid: 10 January 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1136926971

**Mathematical Reviews number (MathSciNet)**

MR2193803

**Zentralblatt MATH identifier**

1152.11343

**Subjects**

Primary: 11C08: Polynomials [See also 13F20]

Secondary: 11R09: Polynomials (irreducibility, etc.) 11Y35: Analytic computations

**Keywords**

Lehmer's problem Mahler measure

#### Citation

Boyd, David W.; Mossinghoff, Michael J. Small Limit Points of Mahler's Measure. Experiment. Math. 14 (2005), no. 4, 403--414. https://projecteuclid.org/euclid.em/1136926971