Zeta Functions on the Unitary Sphere
- 1 January 1952
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 4, 26-30
- https://doi.org/10.4153/cjm-1952-002-4
Abstract
In an earlier paper [5], the author defined a zeta function on the real sphere , whereas in the present paper it is proposed to define one on the unitary sphere where xi's are complex numbers and their complex conjugates. Following E. Cartan, harmonics on the unitary sphere are defined and then a zeta function formed just as in the case of a real sphere. The unitary sphere is seen to behave like an even-dimensional closed manifold, since results similar to the ones proved by the author and A. Pleijel [6] for closed manifolds (of even dimensions) are observed here also.Keywords
This publication has 2 references indexed in Scilit:
- Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian ManifoldsCanadian Journal of Mathematics, 1949
- Sur la détermination d’un système orthogonal complet dans un espace de riemann symétrique closRendiconti del Circolo Matematico di Palermo Series 2, 1929