Minakshisundaram-Pleijel zeta function

Minakshisundaram-Pleijel zeta function

The Minakshisundaram-Pleijel zeta function was introducedby 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}.

References

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


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Minakshisundaram–Pleijel zeta function — The Minakshisundaram–Pleijel zeta function is a zeta function encoding the eigenvalues of the Laplacian of a compact Riemannian manifold. It was introduced by Subbaramiah Minakshisundaram and Åke Pleijel (1949). The case of a compact region… …   Wikipedia

  • Zeta function — A zeta function is a function which is composed of an infinite sum of powers, that is, which may be written as a Dirichlet series::zeta(s) = sum {k=1}^{infty}f(k)^s Examples There are a number of mathematical functions with the name zeta function …   Wikipedia

  • Åke Pleijel — (1913 1989) was a Swedish mathematician.He completed his Ph.D. in Mathematics at Stockholm University in 1940 (with Torsten Carleman as supervisor), and later became Professor of Mathematics at Uppsala University.Åke Pleijel is well known for the …   Wikipedia

  • Subbaramiah Minakshisundaram — (1913 October 12 Trichur – Kerala, 1968 August 13) was an Indian mathematician who worked on heat kernels and parabolic partial differential equations and introduced the Minakshisundaram–Pleijel zeta function. Publications Minakshisundaram, S.;… …   Wikipedia

  • Дзета-функции — Эта страница информационный список. См. также основную статью: Дзета функция Римана В математике дзета функция обычно это функция родственная или аналогичная дзета функции Римана …   Википедия

  • List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”