Toward optimal exponent pairs

Abstract

We quantify the set of known exponent pairs $(k,\ell )$ and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology, we make progress on several open problems, including bounds of the Riemann zeta-function $\hat{I}\P (s)$ in the critical strip, estimates of the moments of $\hat{I}\P (1/2+it)$ and the generalised Dirichlet divisor problem.

38 pages, 2 figures