On a generalisation of the Riemann $\xi$-function

Hirotaka Kobayashi

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arXiv · 2110.12755

On a generalisation of the Riemann $\xi$-function

Hirotaka Kobayashi

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Abstract

It is known that we can construct the meromorphic function $Z_k(s)$ associated with the higher derivative of Hardy's $Z$-function. In this paper, we introduce the entire function derived from $Z_k(s)$, a generalisation of the Riemann $\xi$-function and prove some properties.

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Hirotaka Kobayashi. 2021-10-25. On a generalisation of the Riemann $\xi$-function. https://arxiv.org/abs/2110.12755

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