Room: A580
Time: 2:00-2:50
PM
Speaker:
Tim Trudgian
(University of Lethbridge)
Title: Gram's Law and the zeroes
of the Riemann zeta-function (I)
Abstract: That
all the complex zeroes of the zeta-function lie on the critical line is
the Riemann Hypothesis. Regrettably, the margin for this abstract is
too narrow to write down a proof. The first 15 zeroes on the critical
line were found by Gram in 1903. As a general rule of thumb, he
proposed what is now called 'Gram's Law', a phenomenon by the use of
which one can locate zeroes on the critical line. All subsequent
searches for zeroes on the critical line use this method, in some form
or another. In this seminar I shall summarise the theory one requires
to state Gram's Law, as well as providing motivation for why it might
be true significantly often.
Wednesday,
October 6, 2010
Room: A580
Time: 2:00-2:50
PM
Speaker: Tim
Trudgian (University of Lethbridge)
Title: Gram's Law and the zeroes of the Riemann zeta-function
(II)
Abstract: With Gram's Law clearly defined, I shall develop the
necessary theory to see whether it fails or holds in a positive
proportion of cases. Several versions of Gram's Law hold and fail at
this frequency, and this was my doctoral research at Oxford. Motivation
from random-matrix theory will perhaps indicate the true rate of
success and failure of Gram's Law.
Wednesday,
October 27, 2010
Room: A580
Time: 2:00-2:50
PM
Speaker: Nathan
Ng (University of Lethbridge)
Title: Nonzero values of
Dirichlet L-functions in vertical arithmetic progressions
Abstract: An
open question in analytic number theory is: How do the zeros of a Dirichlet L-function behave in the
critical strip? One might
wonder whether the zeros bunch up or are they very well-spaced.
In particular, is it possible for the zeros to lie
in an arithmetic progression?
In joint work with Greg Martin, we show that many terms of an
arithmetic progression are not zeros of a fixed Dirichlet L-function.
Wednesday,
November 24, 2010
Room: A580
Time: 2:00-2:50
PM
Speaker: Amir
Akbary (University of Lethbridge)
Title: Uniform distribution
of zeros of the Riemann zeta function
Abstract: We
explain the Weyl criterion for the uniform distribution mod 1 of a
sequence of real numbers. As an application of this criterion we
describe a theorem of Hlawka on the uniform distribution mod 1 of the
imaginary parts of the zeros of the Riemann zeta function.
Wednesday,
December 8, 2010
Room: E575
Time: 2:00-2:50
PM
Speaker: Dave
Morris (University of Lethbridge)
Title: Reconstruction from
Vertex-Switching
Abstract: The Reconstruction Conjecture is a famous unsolved
problem in graph theory. We will discuss a related problem that
was partially solved by Richard Stanley in 1985. He used the
Radon Transform, which is a technique that originated in analysis, and
is the mathematical basis of modern CAT scans (used in medical
diagnostics).