Time and Place: Friday, Jan. 28, 10:30-11:30
AM, 4325 HP
Carleton
Speaker: Kevin Hare (University of Waterloo)
Title: The Monic Integer Chebyshev Problem
Abstract: We study the problem of finding monic integer polynomials
$P$ with small supremum norm $||P||_I$
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.
Time and Place: Friday, Feb. 11, 10:30-11:30
AM, KED B015
University of Ottawa
Speaker: Abdelkrim El basraoui (University of Ottawa)
Title: Replicable functions
Abstract: In this talk we present the notion of replicable functions
and provide some examples related to
modular forms.
Time and Place: Friday, March 18,
10:30-11:30 AM, 4325 HP
Carleton
Speaker: Paul Mezo (Carleton University)
Title: Langlands reciprocity
Abstract: We begin by describing the conjecture of Langlands
reciprocity in the context of earlier
reciprocity laws in number theory.
Afterwards we present some ideas which may help in
proving this conjecture.
Time and Place: Monday, March 28, 4:30-5:30 PM, 4325 HP
Carleton
Speaker: Piroska Lakatos (Debrecen University)
Title: On zeroes of self-inversible polynomials
Abstract: Click here
Time and Place: Friday, Apr. 1, 10:30-11:30
AM, 4351 HP
Carleton
Speaker: Ram Murty (Queen's University)
Title: Dirichlet series and hyperelliptic curves
Abstract: We will attach Dirichlet series to hyperelliptic and
superelliptic curves to study the variation
of rational points of twists of such
curves. This is joint work with Jung-Jo Lee.