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arXiv · 2107.14748

On the growth of the $L^p$ norm of the Riemann zeta-function on the line Re$(s)=1$

Johan Andersson
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Abstract

We prove that if $\delta>0$ and $p$ is real then $$ \sup_T \int_T^{T+\delta} |\zeta(1+it)|^p dt <\infty,$$ if and only if $-1 1) $$ which with the exception of an additional $\log \log \log T$ factor in the second estimate coincides with conditional (under the Riemann hypothesis) order estimates. We also prove weaker unconditional order estimates.

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Johan Andersson. 2021-07-30. On the growth of the $L^p$ norm of the Riemann zeta-function on the line Re$(s)=1$. https://arxiv.org/abs/2107.14748

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