The discrete second moment of mixed derivatives of the Riemann zeta function

Benjamin Durkan; C. P. Hughes; Andrew Pearce‐Crump

doi:10.48550/arxiv.2601.06292

The discrete second moment of mixed derivatives of the Riemann zeta function

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Benjamin Durkan, C. P. Hughes, Andrew Pearce‐Crump

DOI: 10.48550/arxiv.2601.06292

Cited by: 0

Abstract

We establish the full asymptotic for the discrete second moment of the Riemann zeta function of mixed derivatives evaluated at the zeta zeros, providing both unconditional and conditional error terms. This was first studied by Gonek, where only the leading order asymptotic was given, later extended by Conrey--Snaith and Milinovich to include the lower order terms for the first derivative. We extend the case of the first derivative to all derivatives.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Identities Advanced Algebra and Geometry

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 9 January 2026
Language: EN
Document type: Preprint