Toward optimal exponent pairs

Trudgian, Timothy; Yang, Andrew

doi:10.1090/mcom/3993

Toward optimal exponent pairs
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by Timothy S. Trudgian and Andrew Yang;

Math. Comp. 94 (2025), 1467-1502

DOI: https://doi.org/10.1090/mcom/3993

Published electronically: July 10, 2024

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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 $\zeta (s)$ in the critical strip, estimates of the moments of $\zeta (1/2 + it)$ and the generalised Dirichlet divisor problem.

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