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Large values of the argument of the Riemann zeta-function and its iterates
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-03-16 , DOI: 10.1016/j.jnt.2021.02.007 Andrés Chirre , Kamalakshya Mahatab
中文翻译:
Riemann zeta函数的参数及其迭代的较大值
更新日期:2021-03-19
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-03-16 , DOI: 10.1016/j.jnt.2021.02.007 Andrés Chirre , Kamalakshya Mahatab
Let be the argument of the Riemann zeta-function at the point in the critical strip. For and , we define where is a specific constant depending on σ and n. Let be a fixed real number. Assuming the Riemann hypothesis, we establish lower bounds for the maximum of near the critical line, on the interval and in a small range of h. This improves some results of the first author and generalizes a result of the authors on . We also give new omega results for , improving a result by Selberg.
中文翻译:
Riemann zeta函数的参数及其迭代的较大值
让 在这一点上成为黎曼zeta函数的参数 在关键地带。为了 和 ,我们定义 在哪里 是取决于σ和n的特定常数。让是固定的实数。假设黎曼假设,我们为下式的最大值建立下界 在临界线附近,在间隔 在h的小范围内。这改善了第一作者的一些结果,并概括了作者在以下方面的结果:。我们还为给出了新的Omega结果,改善了Selberg的结果。