Friday, February 17, 2006
| Speaker |
Mourad Ismail
University of Central Florida |
| Topic |
The Ramanujan Entire Function |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 120 |
Abstract
Ramanujan was a self-educated college dropout who did some of the best mathematics of the twentieth century. He extensively worked on the
$$
F(z)=1+\sum_{n=1}^\infty\frac{(-z)^nq^{n^2}}{(1-q)(1-q^2)\dotsc(1-q^n)},
$$
which we refer to as the Ramanujan entire function. We demonstrate the significance of this function in number theory and analysis and give a new interpretation of the statement
$$
1+\sum_{n=1}^\infty\frac{z^nq^{n^2}}{(1-q)(1-q^2)\dotsc(1-q^n)}
=\prod_{n=1}^\infty\left(1+\frac{zq^{2n-1}}{1-c_1q^n-c_2q^{2n}-\dotsb}\right)
$$
in Ramanujan's lost notebook.
The coefficients \(c_1,c_2,\dotsc\) turned out to have very interesting patterns and many open problems will be mentioned.
Friday, February 10, 2006
| Speaker |
Lesław Skrzypek |
| Topic |
Example of non uniquely minimal projection in \(L_p\), Part II |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 120 |
Friday, February 3, 2006
| Speaker |
Lesław Skrzypek |
| Topic |
Example of non uniquely minimal projection in \(L_p\) |
| Time |
5:00-6:00 p.m. |
| Place |
PHY 120 |