The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann hypothesis fails. In this lecture, we study the Moebius inversion for functions of this type and show how its behavior is related to the distribution of zeros in the half-plane of absolute convergence. Work in collaboration with Amit Ghosh.
Lectures by Faculty
Current educational policy discussions frequently invoke “equality” as the reigning ideal. But how clear a view do we have of what we mean by this? What exactly are we trying to achieve? In this lecture, Danielle Allen, UPS Foundation Professor in the School of Social Science, revisits the question of how to understand the ideal of equality in the context of educational policy.
A knot is more or less what you think it is—a tangled mess of string in ordinary three-dimensional space. In the twentieth century, mathematicians developed a rich and deep theory of knots. And surprisingly, as Edward Witten, Charles Simonyi Professor in the School of Natural Sciences, explains in this lecture, it turned out that many of the most interesting ideas about knots have their roots in quantum physics.
Avi Wigderson, Herbert H. Maass Professor in the School of Mathematics, gave a Friends Forum in October 2011, entitled Randomness and Pseudo-randomness. Is the universe inherently deterministic or probabilistic? Perhaps more importantly, can we tell the difference between the two?