Zeta function and regularized determinant on a disc and on a cone |
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| Institution: | 1. Physics Department, Davidson College, Davidson, NC 28035, USA;2. Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA;1. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, China;2. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300387, China;3. Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China |
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| Abstract: | We give formulas for the analytic extension of the zeta function of the induced Laplacian L on a disc and on a cone. This allows the explicit computation of the value of the zeta function and of its derivative at the origin, and hence we get a formula for the regularized determinant of L. |
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