Department of Mathematics and Computer Science
Number Theory and Combinatorics Seminar
Fall 2015
Talks are at noon on Monday in room C630 of University Hall
For more information, or to receive an email announcement of each week's seminar,
contact Nathan Ng < ng AT cs DOT uleth DOT ca > or Dave Morris <>.
                The next talk:

Nov 30
at noon
in UHall C630
Habiba Kadiri
(University of Lethbridge)
Explicit bounds for $\boldsymbol{\psi(x;q,a)}$
The prime number theorem in arithmetic progressions establishes that, for $a$ and $q$ fixed coprime integers, then $\psi(x;q,a)$ is asymptotic to $\displaystyle\frac{x}{\phi(q)}$ when $x$ is large. We discuss new explicit bounds for the error term $\displaystyle\left|\frac{\psi(x;q,a)-\frac{x}{\phi(q)}}{\frac{x}{\phi(q)}}\right|$, which provide an extension and improvement over the previous work of Ramaré and Rumely. Such results depend on the zeros of the Dirichlet $L$-functions: a numerical verification of the Generalized Riemann Hypothesis up to a given height and explicit zero-free regions. We use the latest results of respectively Platt and Kadiri. In addition our method makes use of smooth weights. This is joint work with Allysa Lumley.

Talks in the series this semester:
(Click on any title for more info, including the abstract. Then click on it again to hide the info.)

Date Speaker Title

Sept 14 everyone Open problem session

Sept 21 Amy Feaver A two-part talk on (1) Sage mathematics software and (2) multiquadratic fields
(King's University)

Sept 28 Dave Morris What is a superrigid subgroup?

Oct 5 Alexey Popov Every operator has almost-invariant subspaces

Oct 19 Alia Hamieh Special Values of Rankin-Selberg $\boldsymbol{L}$-Functions

Oct 26 Farzad Aryan Gaps between zeros of the Riemann zeta function

Nov 2 Nathan Ng The autocorrelation of a multiplicative function

Nov 16 Amir Akbary Lang-Trotter Revisited

Nov 23 Mohammad Bardestani Isotropic quadratic forms and the Borel chromatic number of quadratic graphs
(University of Ottawa)

Nov 30 Habiba Kadiri Explicit bounds for $\boldsymbol{\psi(x;q,a)}$

Dec 7 Joy Morris Title TBA
Past semesters: Fall 2007 Fall 2008 Fall 2009 Fall 2010 Fall 2011 Fall 2012 Fall 2013 Fall 2014
Spring 2008 Spring 2009 Spring 2010 Spring 2012 Spring 2013 Spring 2014 Spring 2015