The set of zeros of the Riemann zeta function as the point spectrum of an operator
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V. V. Kapustin
Translated by: the author - St. Petersburg Math. J. 33 (2022), 661-673
- DOI: https://doi.org/10.1090/spmj/1720
- Published electronically: June 27, 2022
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Abstract:
A possible way of proving the Riemann hypothesis consists of constructing a selfadjoint operartor whose spectrum coincides with the set $\{z\,: \, |\operatorname {Im}z|<\frac 12, \ \zeta \big (\frac {1}{2}-iz\big )=0\}$. In the paper we construct a rank-one perturbation of a selfadjoint operator related to a certain canonical system for which a similar property is fulfilled.References
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Bibliographic Information
- V. V. Kapustin
- Affiliation: St. Petersburg Department of the Steklov Mathematical Institute, RAS, Fontanka 27, St. Petersburg 191023, Russia
- Email: kapustin@pdmi.ras.ru
- Received by editor(s): June 23, 2020
- Published electronically: June 27, 2022
- Additional Notes: The work was partially supported by RFBR grant no. 19-01-00565a
- © Copyright 2022 American Mathematical Society
- Journal: St. Petersburg Math. J. 33 (2022), 661-673
- MSC (2020): Primary 30H45
- DOI: https://doi.org/10.1090/spmj/1720
Dedicated: Dedicated to the memory of Vladimir Marikhin