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Zeta Functions on the Unitary Sphere

Published online by Cambridge University Press:  20 November 2018

S. Minakshisundaram
S. Minakshisundaram*
Affiliation:
Waltair, S. India
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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.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 26 - 30
Copyright
Copyright © Canadian Mathematical Society 1952

References

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