A Novel Integral Equation for the Riemann Zeta Function and Large t -Asymptotics

Konstantinos Kalimeris and Athanassios S. Fokas
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Konstantinos Kalimeris: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
Athanassios S. Fokas: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK

Mathematics, 2019, vol. 7, issue 7, 1-18

Abstract: Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta function. Then, we introduce the machinery needed to obtain an estimate for the solution of this equation. This approach suggests a substantial improvement of the current large t - asymptotics estimate for ζ 1 2 + i t .

Keywords: riemann zeta function; asymptotics; exponential sums (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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