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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Gandalf (Pure Maths Student Seminar): Integer valued polynomials

Presented by Anna Szumowicz, Durham

27 April 2016 16:00 in CM221

The polynomial ${X \choose m}$, where $m$ is a natural number is an example of a polynomial which takes integer values on $\mathbb{Z}$ even though its coefficients are not integer. A polynomial $f\in \mathbb{Q}[x]$ with the property $f(\matbb{Z}\subset \mathbb{Z})$ is called integer-valued. If $f$ is of degree at most $n$, then it is enough to check that $f({0,...n}) $ takes values in $\mathbb{Z}$ to know that $f$ is integer-valued. A finite set $A$ is called $n$-universal if $f(A)\subset \mathbb{Z}$ implies that $f$ is integer-valued for every $f$ of degree at most $n$. I will talk about $n$-universal sets when $\mathbb{Q}$ is replaced by a number field.

Contact or for more information

Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.

Content from previous talks is available at the gandalf seminar home page.