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On the Hilbert space derived from the Weil distribution | | Masatoshi Suzuki
; | | Date: |
1 Jan 2023 | | Abstract: | We study the Hilbert space obtained by completing the space of all smooth and
compactly supported functions on the real line with respect to the hermitian
form arising from the Weil distribution under the Riemann hypothesis. It turns
out that this Hilbert space is isomorphic to a de Branges space by a
composition of the Fourier transform and a simple map. This result is also
applied to state a new equivalence condition for the Riemann hypothesis. | | Source: | arXiv, 2301.00421 | | Services: | Forum | Review | PDF | Favorites | |
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