We prove that there are arbitrarily large values of t such that {equation presented}. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararajan. Our proof uses a new variant of the "long resonator" method. While earlier implementations of this method crucially relied on a "sparsification" technique to control the mean-square of the resonator function, in the present paper we exploit certain self-similarity properties of a specially designed resonator function.

Extreme Values of the Riemann Zeta Function on the 1-Line

Munsch M.
2019-01-01

Abstract

We prove that there are arbitrarily large values of t such that {equation presented}. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararajan. Our proof uses a new variant of the "long resonator" method. While earlier implementations of this method crucially relied on a "sparsification" technique to control the mean-square of the resonator function, in the present paper we exploit certain self-similarity properties of a specially designed resonator function.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1091983
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