Constellations of zeroes of the Riemann zeta-function

Description:

Current zero-free region techniques for the zeta-function assume that if there is a zero close to the one-line, then certain inequalities (the strongest of which involve a trigonometric argument dating back to de la Vallee Poussin in the 19th century) must break. Conclusion: there cannot be a zero too close to the one-line. Levinson outlined an argument (developed further by Montgomery) to leverage a little more out of this approach. This assumes that if there is an isolated zero near the one line, then this repels other zeroes. This has not yet been put onto an explicit footing. Given current zero-free regions seem close to being fully optimised, this extra ingredient would be exceptionally useful in applications.

This project would align with the current interests of the number theory group at the School of Science, UNSW Canberra.