Evaluation of spherical GJMS determinants

J. S. Dowker, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd-dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. This is formalised and expanded by an analytical treatment of the integral which produces an explicit combinatorial expression directly in terms of the Riemann zeta function, and log. 2. An incidental byproduct is a (known) expression for the central factorial coefficients in terms of higher Bernoulli numbers.

Original languageEnglish
Pages (from-to)51-60
Number of pages10
JournalJournal of Geometry and Physics
StatePublished - 1 Nov 2015


  • Determinants
  • GJMS operator
  • Higher Bernoulli numbers
  • Riemann zeta function

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology


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