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Toward optimal exponent pairs
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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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Cited by 1 Pith paper
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New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
By systematically codifying and optimizing known exponent relations in the ANTEDB database, the paper derives four new exponent pairs, new zero density bounds, and new additive energy bounds for the Riemann zeta-function.
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