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    • ξζrelation

      M Krishna

      Volume 109 Issue 4 November 1999 pp 379-383

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/109/04/0379-0383

    • Keywords

       

      Krein spectral shift; Riemann zeta

    • Abstract

       

      In this note we prove a relation between the Riemann Zeta function, ζ and the ξ function (Krein spectral shift) associated with the harmonic oscillator in one dimension. This gives a new integral representation of the zeta function and also a reformulation of the Riemann hypothesis as a question inL1(ℝ).

    • Author Affiliations

       

      M Krishna1

      1. Institute of Mathematical Sciences, Taramani, Chennai - 600113, India

    • Dates

       
      Published
      November 1999
      Manuscript received
      27 January 1999
      Manuscript revised
      13 July 1999

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