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Lower bounds for the Riemann zeta function on short intervals of the critical line

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Abstract

We consider a problem first studied by Karatsuba, of giving lower bounds for the Riemann zeta function in short intervals of the critical line. We give an upper bound for the measure of the set where a lower bound of Karatsuba and Garaev fails to hold, and we also show a conjecture of Karatsuba holds for almost all values of t.

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  1. Department of Pure Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia

    Bryce Kerr

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  1. Bryce Kerr
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Correspondence to Bryce Kerr.

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Kerr, B. Lower bounds for the Riemann zeta function on short intervals of the critical line. Arch. Math. 105, 45–53 (2015). https://doi.org/10.1007/s00013-015-0777-y

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  • DOI: https://doi.org/10.1007/s00013-015-0777-y

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