School of Mathematics and Statistics |
Department of Mathematics and Statistics |

**NUMBER THEORY SEMINAR**

**Winter 2005**

on an interval $I$. The monic integer trasfinite diameter $t_{\mathrm{M}}(I)$ is defined as

t_{\mathrm{M}}(I) := {\inf_P ||P||_I^{1/\deg(P)},$

where the infimum is taken over all non-constant monic polynomials with integer coefficients. We

;show that if $I$ has length $l$ then $t_{\mathrm{M}}(I) = 1/2$.

We also consider the problem of determining $t_{\mathrm{M}}(I)$ when $I$ is a Farey interval.

We give some partial results, which support a conjecture of Borwein, Pinner and Pritsker concerning

this value.

modular forms.

reciprocity laws in number theory. Afterwards we present some ideas which may help in

proving this conjecture.

of rational points of twists of such curves. This is joint work with Jung-Jo Lee.

Paul Mezo

mezo@math.carleton.ca

Tel. 520-2600 ext 2156