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 <Dave.Morris@uleth.ca>. |
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.) |
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 |