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Dr. Pi
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Bounds of zeta function near $\Re(s)=1$

Richert proved in https://link.springer.com/article/10.1007/BF01399533 that $$ \zeta(s) =O\left( |\Im(s)|^{100(1-\Re(s))^{3/2}} (\log |\Im(s)|)^{2/3}\right)$$ uniformly in the region $\Re(s)\in [1/2,1], |\Im(s)|\geq 2.$ The exponent $100$ has been improved to $4.45$ by Ford https://arxiv.org/abs/1910.08209.

My question is whether the constant $4.45$ has been further improved?

Dr. Pi
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