Minakshisundaram-Pleijel zeta function

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The Minakshisundaram-Pleijel zeta function was introduced by the mathematicians Subbaramiah Minakshisundaram and Åke Pleijel.

For a surface with eigenvalues of the Laplace-Beltrami operator \lambda_1, \lambda_2, \cdots

it is given for Re(s) > 1 by

Z(s) = \sum_{n=1}^{\infty} \vert \lambda_{n} \vert^{-s}.

[edit] References

  • Minakshisundaram, S.; Pleijel, Å. Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds. Canadian J. Math. 1, (1949). 242--256.