Some analytic continuations of the Barnes zeta function in two and higher dimensions

E. Elizalde

    Research output: Contribution to journalArticleResearchpeer-review

    4 Citations (Scopus)


    Formulas for the analytic continuation of the Barnes zeta function, and some affine extensions thereof, in two and more dimensions, are constructed. The expressions are used to deal with determinants of multidimensional harmonic oscillators. An example is therewith obtained of the multiplicative anomaly (or defect), associated with the most common definition (due to Ray and Singer [D.B. Ray, Reidemeister torsion and the Laplacian on lens spaces, Adv. Math. 4 (1970) 109-126; D.B. Ray, I.M. Singer, R-torsion and the Laplacian on Riemannian manifolds, Adv. Math. 7 (1971) 145-201; D.B. Ray, I.M. Singer, Analytic torsion for complex manifolds, Ann. Math. 98 (1973) 154-177]) of determinant of a pseudodifferential operator admitting a zeta function [M. Kontsevich, S. Vishik, Geometry of determinants of elliptic operators, in: Functional Analysis on the Eve of the 21st Century, vol. 1, 1995, pp. 173-197]. © 2006 Elsevier Inc. All rights reserved.
    Original languageEnglish
    Pages (from-to)141-152
    JournalApplied Mathematics and Computation
    Issue number1 SPEC. ISS.
    Publication statusPublished - 1 Apr 2007


    • Barnes zeta function
    • Determinant
    • Hurwitz (or generalized) zeta
    • Multiplicative anomaly (or defect)
    • Quantum harmonic oscillators


    Dive into the research topics of 'Some analytic continuations of the Barnes zeta function in two and higher dimensions'. Together they form a unique fingerprint.

    Cite this