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AN UPPER BOUND FOR DISCRETE MOMENTS OF THE DERIVATIVE OF THE RIEMANN ZETA‐FUNCTION
Mathematika ( IF 0.8 ) Pub Date : 2020-04-01 , DOI: 10.1112/mtk.12008
Scott Kirila 1
Affiliation  

Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where $k$ is a positive real number. Our upper bound agrees with conjectures of Gonek and Hejhal and of Hughes, Keating, and O'Connell. This sharpens a result of Milinovich. Our proof builds upon a method of Adam Harper concerning continuous moments of the zeta-function on the critical line.

中文翻译:

黎曼 ZETA 函数导数的离散矩的上界

假设黎曼假设,我们为黎曼 zeta 函数在非平凡零点处的导数的第 2k$ 个离散矩建立一个上限,其中 $k$ 是一个正实数。我们的上限与 Gonek 和 Hejhal 以及 Hughes、Keating 和 O'Connell 的猜想一致。这加剧了米利诺维奇的结果。我们的证明建立在 Adam Harper 关于临界线上 zeta 函数的连续矩的方法之上。
更新日期:2020-04-01
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