# Vinogradov's Integral and Bounds for the Riemann Zeta Function

@article{Ford2002VinogradovsIA,
title={Vinogradov's Integral and Bounds for the Riemann Zeta Function},
author={Kevin Ford},
journal={Proceedings of The London Mathematical Society},
year={2002},
volume={85},
pages={565-633}
}
• K. Ford
• Published 2002
• Mathematics
• Proceedings of The London Mathematical Society
The main result is an upper bound for the Riemann zeta function in the critical strip: $\zeta(\sigma + it) \le A|t|^{B(1 - \sigma)^{3/2}} \log^{2/3} |t|$ with $A = 76.2$ and $B = 4.45$, valid for $\frac12 \le \sigma \le 1$ and $|t| \ge 3$. The previous best constant $B$ was 18.5. Tools include a variant of the Korobov–Vinogradov method of bounding exponential sums, an explicit version of T. D. Wooley's bounds for Vinogradov's integral, and explicit bounds for mean values of exponential sums… Expand
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