## Experimental Mathematics

- Experiment. Math.
- Volume 13, Issue 3 (2004), 331-341.

### On the Height of the Sylvester Resultant

Carlos D'Andrea and Kevin G. Hare

#### Abstract

Let $n$ be a positive integer. We consider the Sylvester resultant of $f$ and $g,$ where $f$ is a generic polynomial of degree 2 or 3 and $g$ is a generic polynomial of degree $n.$ If $f$ is a quadratic polynomial, we find the resultant's height. If $f$ is a cubic polynomial, we find tight asymptotics for the resultant's height.

#### Article information

**Source**

Experiment. Math., Volume 13, Issue 3 (2004), 331-341.

**Dates**

First available in Project Euclid: 22 December 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1103749841

**Mathematical Reviews number (MathSciNet)**

MR2103331

**Zentralblatt MATH identifier**

1116.11046

**Subjects**

Primary: 11G50: Heights [See also 14G40, 37P30]

Secondary: 12Y05: Computational aspects of field theory and polynomials

**Keywords**

Sylvester resultants heights quadratic and cubic polynomials

#### Citation

D'Andrea, Carlos; Hare, Kevin G. On the Height of the Sylvester Resultant. Experiment. Math. 13 (2004), no. 3, 331--341. https://projecteuclid.org/euclid.em/1103749841