|Date: Monday, April 02, 2018
Location: 4088 East Hall (4:10 PM to 5:30 PM)
Title: Recent progress on the de Bruijn-Newman constant
Abstract: N.G. de Bruijn introduced a one-parameter family of entire functions $H_t(z)$ with properties that i) the zeros of $H_0(z)$ characterize the zeros of the Riemann zeta function -- the Riemann hypothesis ends up being equivalent to the claim that $H_0(z)$ has only real zeros -- and ii) there exists a number $\Lambda$, known as the de Bruijn-Newman constant, such that $H_t(z)$ has only real zeros exactly when $t \geq \Lambda$. The Riemann hypothesis is equivalent to the claim that $\Lambda \leq 0$.
De Bruijn in 1950 showed that $\Lamdba \leq 1/2$, while C. Newman in 1976 proved that $\Lambda > -\infty$ and conjectured that $\Lambda \geq 0$, a curious complement to the Riemann hypothesis. In this talk I will outline some of what's known about the zeros of the Riemann zeta function and the functions $H_t(z)$ and discuss a recent proof joint with Terence Tao of Newman's conjecture.
Speaker: Brad Rodgers