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Mathematics & Statistics

Analysis
(Leader: Prof. Boris Shekhtman )

Friday, February 17, 2006

Title
Speaker

Time
Place

The Ramanujan Entire Function
Mourad Ismail
University of Central Florida
5:00pm-6:00pm
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

Title
Speaker
Time
Place

Example of non uniquely minimal projection in \(L_p\), Part II
Lesław Skrzypek
5:00pm-6:00pm
PHY 120

Friday, February 3, 2006

Title
Speaker
Time
Place

Example of non uniquely minimal projection in \(L_p\)
Lesław Skrzypek
5:00pm-6:00pm
PHY 120