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Science China Mathematics

, Volume 62, Issue 11, pp 2317–2330 | Cite as

On spectral theory of the Riemann zeta function

  • Xian-Jin LiEmail author
Articles
  • 35 Downloads

Abstract

Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-Pólya space. It has geometric multiplicity one. A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given. It is an analogue of the Selberg transform in Selberg’s trace formula. Elements of the Hilbert-Pólya space are characterized by the Poisson summation formula.

Keywords

Hilbert-Pólya space spectrum of operators zeros of zeta function 

MSC(2010)

46A03 11M26 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA

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