Zeta function of self-adjoint operators on surfaces of revolution. (20th March 2015)

• Record Type: Journal Article
• Authors: Lu, Tianshi; Jeffres, Thalia; Kirsten, Klaus
• Is Part Of: Journal of physics. Volume 48:Number 14(2015)
• Publication Date: 2015-03-20
• Subjects: zeta function -- self-adjoint -- contour integral -- WKB; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/14/145204
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this article we analyze the zeta function for the Laplace operator on a surface of revolution. A variety of boundary conditions, separated and unseparated, are considered. Formulas for several residues and values of the zeta function as well as for the determinant of the Laplacian are obtained. The analysis is based upon contour integration techniques in combination with a WKB analysis of solutions of related initial value problems.