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

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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… Click to show full 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: zeta function; riemann zeta; integral equation; equation; novel integral; large asymptotics

Journal Title: Mathematics
Year Published: 2019

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