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

Fall 2007

Time and Place: Monday, Oct. 22, 3pm-4pm, room KED B-015 Ottawa

Speaker: Arnaud Chadozeau (CRM, Université de Montréal)

Title: Distribution of numbers coprime to a given integer in small intervals


Form work of Montgomery and Vaughan, the number of integers coprime
to a given modulus q in an interval of length h is known to have
Gaussian distribution of mean and variance equal to h phi(q)/q,
provided h is suitably large. (Here, phi is the Euler totient function.)
We refine this statement for moduli q free of small prime factors (less than h).

Time and Place: Monday, Nov. 5, 3pm-4pm, room KED B-015 Ottawa

Speaker: Gary Walsh (University of Ottawa)

Title: Arithmetical properties of a sequence of integers related to a family of simultaneous Pell equations


We discuss necessary conditions for the existence of an integral solution to a
system of Pell equations, and some arithmetical results pertaining to the coefficients
of such solvable systems, improving upon recent work of Zhenfu Cao and his colleagues.

Time and Place: Monday, Nov. 12, 3pm-4pm, room KED B-015 Ottawa

Speaker: Youness Lamzouri (Université de Montréal)

Title: The two dimensional distribution of values of the Riemann zeta function on the one-line


In this talk we present several results on the joint distribution function of the argument
and the norm of the Riemann zeta function on the one line. Similar results for Dirichlet
L-functions at one are also given.

Here is the longer version of the abstract .

Time and Place: Monday, Nov. 26, 3pm-4pm, room KED B-015 Ottawa

Speaker: Shanta Laishram (University of Waterloo)

Title: Squares in Arithmetic Progression


A result of Fermat states that there are no four squares in an arithmetic
progression and Euler gave a general result that product of four terms of an
arithmetic progression is never a square. Hirata-Kohno, Laishram, Shorey
and Tijdeman extended Euler's result upto $109$ terms. For this, we
consider the Diophantine equation n(n+d)...(n+(k-1)d)=y^2
with n>= 1, d>= 2, k >= 3 and gcd(n, d)=1. In this talk, I
will give some history and discuss the above result and related results. In fact, in
a joint work with Shorey, we show that the above equation has no solution when
d <= 10^{10} or d has at most five prime divisors.

Time and Place: Monday, Dec. 3, room KED B-015 Ottawa

Speaker: Brandon Fodden (PIMS/University of Lethbridge)

Title: Diophantine equations and the generalized Riemann hypothesis
Abstract: We show how methods from the negative solution to Hilbert's tenth problem
may be used to show certain statements are equivalent to the unsolvability
of a Diophantine equation. When this happens, we will say the statement is
Diophantine. We show that the generalized Riemann hypothesis for a number
field is Diophantine. We also show the statement 'the generalized Riemann
hypothesis holds for every number field' is Diophantine. That is, there is
a Diophantine equation which has no solutions if and only if the
generalized Riemann hypothesis holds for every number field.


For further information on the seminar please contact:
Nathan Ng
nng362 at
Tel. 613-562-5800 ext 3515
Damien Roy
droy at
Tel. 613-562-5800 ext 3504