English

A note on the large values of $|\zeta^{(\ell)}(1+{\rm i}t)|$

Number Theory 2022-03-31 v1

Abstract

We investigate the large values of the derivatives of the Riemann zeta function ζ(s)\zeta(s) on the 1-line. We give a larger lower bound for maxt[T,2T]ζ()(1+it)\max_{t\in[T,2T]}|\zeta^{(\ell)}(1+{\rm i} t)|, which improves the previous result established by Yang.

Keywords

Cite

@article{arxiv.2203.16086,
  title  = {A note on the large values of $|\zeta^{(\ell)}(1+{\rm i}t)|$},
  author = {Zikang Dong and Bin Wei},
  journal= {arXiv preprint arXiv:2203.16086},
  year   = {2022}
}

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6 pages