Carleton University
School of Mathematics and Statistics
University of Ottawa
Department of Mathematics and Statistics

NUMBER THEORY SEMINAR
Winter 2005


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.

For further information on the seminar please contact:
Paul Mezo
mezo@math.carleton.ca
Tel. 520-2600 ext 2156