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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Beurling's theorem, Davenport's formula, and the Riemann hypothesis


Author: V. V. Kapustin
Translated by: V. V. Kapustin
Original publication: Algebra i Analiz, tom 30 (2018), nomer 6.
Journal: St. Petersburg Math. J. 30 (2019), 917-932
MSC (2010): Primary 11M26
DOI: https://doi.org/10.1090/spmj/1577
Published electronically: September 16, 2019
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Abstract: Various unitarily equivalent models are treated that are related to the approach of Beurling and Nyman to the Riemann hypothesis about zeros of the Riemann zeta function. The relationship is discussed between the Riemann hypothesis and properties of the subspace of the weighted Hilbert space $ L^2_{1/x^2}(0, 1)$ generated by the functions $ \rho (nx)$, $ n=1, 2, \dots $, where $ \rho (\,\cdot \,)$ denotes the fractional part of a real number.


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Additional Information

V. V. Kapustin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
Email: kapustin@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1577
Keywords: Riemann zeta function, approach of Beurling--Nyman to the Riemann hypothesis
Received by editor(s): December 7, 2017
Published electronically: September 16, 2019
Additional Notes: The work is partially supported by RFBR grant no. 16-01-00635-a
Article copyright: © Copyright 2019 American Mathematical Society