Zeros of a polynomial of $\zeta^{(j)}(s)$

Tomokazu Onozuka

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arXiv · 1811.05277

Zeros of a polynomial of $\zeta^{(j)}(s)$

Tomokazu Onozuka

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Abstract

We give results on zeros of a polynomial of $\zeta(s),\zeta'(s),\ldots,\zeta^{(k)}(s)$. First, we give a zero free region and prove that there exist zeros corresponding to the trivial zeros of the Riemann zeta function. Next, we estimate the number of zeros whose imaginary part is in $(1,T)$. Finally, we study the distribution of the real part and the imaginary part of zeros, respectively.

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Tomokazu Onozuka. 2018-11-13. Zeros of a polynomial of $\zeta^{(j)}(s)$. https://arxiv.org/abs/1811.05277

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