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:

Sept 22
at noon
in UHall B660
Farzad Aryan
(University of Lethbridge)
On Binary and Quadratic Divisor Problem
Let \(d(n)=\sum_{d|n} 1\). This is known as the divisor function. It counts the number of divisors of an integer. Consider the following shifted convolution sum $$ \sum_{an-m=h}d(n) \, d(m) \, f(an, m), $$ where \(f\) is a smooth function which is supported on \([x, 2x]\times[x, 2x]\) and oscillates mildly. In 1993, Duke, Friedlander, and Iwaniec proved that $$ \sum_{an-m=h}d(n) \, d(m) \, f(an, m) = \textbf{Main term}(x)+ \mathbf{O}(x^{0.75}).$$ Here, we improve (unconditionally) the error term in the above formula to \(\mathbf{O}(x^{0.61})\), and conditionally, under the assumption of the Ramanujan-Petersson conjecture, to \(\mathbf{O}(x^{0.5}).\) We will also give some new results on shifted convolution sums of functions coming from Fourier coefficients of modular forms.

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 Felix Title TBA

Oct 6 Nathan Ng Title TBA

Oct 20 Sean Fitzpatrick Title TBA

Oct 27 Kevin Henriot Title TBA

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