Toward optimal exponent pairs

Timothy S. Trudgian; Andrew Yang

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arXiv · 2306.05599

Toward optimal exponent pairs

Timothy S. Trudgian·Andrew Yang

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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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Timothy S. Trudgian, Andrew Yang. 2023-06-09. Toward optimal exponent pairs. https://arxiv.org/abs/2306.05599

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