The goal is to develop numerical methods to verify and extend conjectures about the large values of the Riemann zeta function in short intervals. The detailed objectives are:
- Learn about the Riemann zeta function and its relation to the distribution of prime numbers.
- Develop numerical simulations of the Riemann zeta function (referred to as Random Zeta below). Random Zeta is a stochastic process.
- Analyze the large values of Random Zeta for several interval lengths. In particular, verify the known conjecture for such intervals.
- Develop numerical simulations for the Riemann zeta function itself.
This project is supported through the NSF CAREER grant #1653602 : Statistics of Extrema in Complex and Disordered Systems