Toward optimal exponent pairs

2023/06/09 by Trudgian, Timothy S., Yang, Andrew · 1 citation
#11L07 #11M06 #11T23 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.05599

Abstract

We quantify the set of known exponent pairs (k, ℓ) 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 ζ(s) in the critical strip, estimates of the moments of ζ(1/2 + it) and the generalised Dirichlet divisor problem.

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