论文标题
Riemann Zeta功能及其迭代的论点的巨大价值
Large values of the argument of the Riemann zeta-function and its iterates
论文作者
论文摘要
令$ s（σ，t）= \ frac {1}π\argζ（σ+it）$为riemann zeta函数的参数，点$σ+it $ riemann zeta-function。对于$ n \ geq 1 $和$ t> 0 $，我们定义\ begin {equination*} s_ {n}（σ，σ，t）= \ int_0^t s_ {n-1} {n-1}（σ，τ）\，dτ+δ__ $σ$和$ n $。令$ 0 \ leqβ<1 $为固定的实际数字。假设假设是$ s_n（σ，t+h）-s_n（σ，t）$在临界线附近的最大$ s_n（σ，t+h）$，以$ t^β\ leq t \ leq t $以及在$ h $ $ h $的小范围内建立下限。这改善了第一作者的一些结果，并概括了作者在$ s（t）$上的结果。我们还为$ s_n（t）$提供了新的Omega结果，从而改善了Selberg的结果。
Let $S(σ,t)=\frac{1}π\argζ(σ+it)$ be the argument of the Riemann zeta-function at the point $σ+it$ in the critical strip. For $n\geq 1$ and $t>0$, we define \begin{equation*} S_{n}(σ,t) = \int_0^t S_{n-1}(σ,τ) \,dτ+ δ_{n,σ\,}, \end{equation*} where $δ_{n,σ}$ is a specific constant depending on $σ$ and $n$. Let $0\leq β<1$ be a fixed real number. Assuming the Riemann hypothesis, we establish lower bounds for the maximum of $S_n(σ,t+h)-S_n(σ,t)$ near the critical line, on the interval $T^β\leq t \leq T$ 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.
