Number Theory Seminar (2011-10-06): Computations of the Riemann zeta function
Speaker
Jon Bober (University of Washington)
Abstract
I'll give a historical overview of computations of the zeta function on the critical line and then describe some recent computations from the past year. Mostly this will focus on an implementation of Ghaith Hiary's nt(2f)20111006/latex_b6692a2ebd3c389f7a86f177222876337462456e_p1.png "$O(t^{1/3})$")
method for computing nt(2f)20111006/latex_9f10e9b601cfbc212dcd99b0458b65429144189c_p1.png "$\zeta(1/2 + it)$")
and computations that Hiary and I have been running using it. Highlights will include the nt(2f)20111006/latex_6bd77f8e5690adf5f399356f33965be2a2140975_p1.png "$10^{32}$")
nd zero, values of nt(2f)20111006/latex_417fc46cfe7f039b55380ff9b1a4ed8b9ed11d59_p1.png "$|\zeta(1/2 + it)|$")
larger than 14000, and some record observations of irregularities in the distribution of zeros.