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The Dirichlet divisor problem,traces and determinants for complex powers of the twisted bi-Laplacian |
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| Authors: | Xiaoxi Duan M.W. Wong |
| Affiliation: | Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada |
| Abstract: | Estimating the counting function for the eigenvalues of the twisted bi-Laplacian leads to the Dirichlet divisor problem, which is then used to compute the trace of the heat semigroup and the Dixmier trace of the inverse of the twisted bi-Laplacian. The zeta function regularizations of the traces and determinants of complex powers of the twisted bi-Laplacian are computed. A formula for the zeta function regularizations of determinants of heat semigroups of complex powers of the twisted bi-Laplacian is given. |
| Keywords: | Twisted bi-Laplacian Dirichlet divisor problem Counting function Complex powers Zeta function Riemann zeta function Trace Heat semigroup Dixmier trace Inverse Zeta function regularizations Determinant |
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