Zeta Functions on the Unitary Sphere

Type: Article

Publication Date: 1952-01-01

Citations: 9

DOI: 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 x i '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.

Locations

  • Canadian Journal of Mathematics - View - PDF

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