Department of Mathematics and Computer Science
Number Theory and Combinatorics Seminar
Fall 2014
Talks are at noon on Monday in room B660 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:

Oct 6
at noon
in UHall B660
Nathan Ng
(University of Lethbridge)
Inclusive Prime Number Races
Let \(\pi(x;q,a)\) denote the number of primes up to \(x\) that are congruent to \(a \pmod{q}\). A "prime number race", for fixed modulus \(q\) and residue classes \(a_1,\ldots,a_r\), investigates the system of inequalities $$\pi(x;q,a_1)>\pi(x;q,a_2)> \cdots >\pi(x;q,a_r). $$ We expect that this system should have arbitrarily large solutions \(x\), and moreover we expect the same to be true no matter how we permute the residue classes \(a_j\); if this is the case, the prime number race is called "inclusive". Rubinstein and Sarnak proved conditionally that every prime number race is inclusive; they assumed not only the generalized Riemann hypothesis but also a strong statement about the linear independence of the zeros of Dirichlet L-functions. We show that the same conclusion can be reached with a substantially weaker linear independence hypothesis. This is joint work with Greg Martin.

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 8 everyone Open problem session

Sept 15 Joy Morris Colour-permuting automorphisms of Cayley graphs

Sept 22 Farzad Aryan On Binary and Quadratic Divisor Problem

Sept 29 Adam Tyler Felix Common divisors of the index and order of \(a\) modulo \(p\)

Oct 6 Nathan Ng Inclusive Prime Number Races

Oct 20 Sean Fitzpatrick Title TBA

Oct 27 Kevin Henriot Linear equations in dense subsets of the squares

Nov 3 Amir Akbary Title TBA

Nov 10 James Parks Title TBA

Nov 17 Manoj Kumar Title TBA

Nov 24 Soroosh Yazdani Title TBA

Dec 1 Speaker TBA Title TBA
Past semesters: Fall 2007 Fall 2008 Fall 2009 Fall 2010 Fall 2011 Fall 2012 Fall 2013
Spring 2008 Spring 2009 Spring 2010 Spring 2012 Spring 2013 Spring 2014