Trace Formulas Applied to the Riemann ζ-Function

  • Mark S. Ashbaugh
  • Fritz Gesztesy
  • Lotfi Hermi
  • Klaus KirstenEmail author
  • Lance Littlejohn
  • Hagop Tossounian
Part of the CRM Series in Mathematical Physics book series (CRM)


We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.


Dirichlet Laplacian Trace class operators Trace formulas Riemann zeta function Spectral theory 



We are indebted to the anonymous referee for kindly bringing references [24] and [27] to our attention.

Klaus Kirsten was supported by the Baylor University Summer Sabbatical and Research Leave Program.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mark S. Ashbaugh
    • 1
  • Fritz Gesztesy
    • 2
  • Lotfi Hermi
    • 4
  • Klaus Kirsten
    • 5
    Email author
  • Lance Littlejohn
    • 2
  • Hagop Tossounian
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Department of MathematicsBaylor UniversityWacoUSA
  3. 3.Center for Mathematical ModelingUniversidad de ChileSantiagoChile
  4. 4.Department of Mathematics and StatisticsFlorida International UniversityMiamiUSA
  5. 5.GCAP-CASPER, Department of MathematicsBaylor UniversityWacoUSA

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