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- W3033995794 abstract "Let $S(sigma,t)=frac{1}{pi}argzeta(sigma+it)$ be the argument of the Riemann zeta-function at the point $sigma+it$ in the critical strip. For $ngeq 1$ and $t>0$, we define begin{equation*} S_{n}(sigma,t) = int_0^t S_{n-1}(sigma,tau) ,dtau + delta_{n,sigma,}, end{equation*} where $delta_{n,sigma}$ is a specific constant depending on $sigma$ and $n$. Let $0leq beta<1$ be a fixed real number. Assuming the Riemann hypothesis, we establish lower bounds for the maximum of $S_n(sigma,t+h)-S_n(sigma,t)$ near the critical line, on the interval $T^betaleq t leq T$ and in a small range of $h$. This improves some results of the first author and generalizes a result of the authors on $S(t)$. We also give new omega results for $S_n(t)$, improving a result by Selberg." @default.
- W3033995794 created "2020-06-12" @default.
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- W3033995794 date "2020-06-08" @default.
- W3033995794 modified "2023-10-16" @default.
- W3033995794 title "Large values of the argument of the Riemann zeta-function and its iterates" @default.
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