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arXiv · 2107.03191

An extension to the complex plane of the Riemann-Siegel Z function

Giovanni Lodone
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Abstract

The usual Riemann-Siegel Z(t) is a real-valued function. We construct a complex function depending from t and from distance from critical line. It is linked to Riemann Xi(s) function by the same real scaling factor of the usual Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of Riemann-Siegel Z(t) on the critical line, while this result covers at least the whole critical strip.

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Giovanni Lodone. 2021-07-07. An extension to the complex plane of the Riemann-Siegel Z function. https://arxiv.org/abs/2107.03191

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