This is joint work with Mathew Rogers.
Roberts' conjecture has also been proved independently by Bhargava, Shankar, and Tsimerman. Their proof uses the geometry of numbers, while our proof uses the analytic theory of Shintani zeta functions. We will also discuss a combined approach which yields further improved error terms.
This is joint work with Takashi Taniguchi.
Such an estimate is used when approximating the potential contribution of zeroes off the critical line. This is used in explicit versions of the prime number theorem and the zero-free region. In this talk I will outline a sharpening of Rosser's result.