Mean square of the derivatives of Hardy's Z-function

Let Z(t) be Hardy's Z-function. We shall study the asymptotic behavior of the derivatives of Z(t) with more precise error term. As an application of our formula, we shall give a proof of Hall's conjecture on the order of the error term in the mean square formula of Z(k)(t).

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of mathematical analysis and applications 2020-05, Vol.485 (1), p.123772, Article 123772
Hauptverfasser:	Minamide, T. Makoto, Tanigawa, Yoshio
Format:	Artikel
Sprache:	eng
Schlagworte:	Derivatives of Hardy's Z-function Hardy's Z-function Mean square estimate The Riemann-Siegel formula
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Beschreibung
Zusammenfassung:	Let Z(t) be Hardy's Z-function. We shall study the asymptotic behavior of the derivatives of Z(t) with more precise error term. As an application of our formula, we shall give a proof of Hall's conjecture on the order of the error term in the mean square formula of Z(k)(t).
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2019.123772