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On the Berry-Keating Operator
[Submitted on 23 Jun 2026] · 2026-06-24 · via math updates on arXiv.org

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Abstract:We review here two different viewpoints on the Berry-Keating operator $H_{BK}$, whose connection to the Riemann hypothesis remains an intriguing and not yet fully understood question, despite considerable attention in the recent literature. In particular, we propose two somehow complementary views to $H_{BK}$: the first is based on a purely Hilbertian point of view, on dilation operators and on the Mellin transform. The second is a distributional approach, with a specific view to ladder operators, generalized eigenstates of $H_{BK}$, and generalized coherent states.

Submission history

From: Fabio Bagarello Dr. [view email]
[v1] Tue, 23 Jun 2026 10:43:48 UTC (14 KB)

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