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A property of new coordinates defining augmented Schottky spaces

Published online by Cambridge University Press:  22 January 2016

Hiroki Sato
Hiroki Sato*
Affiliation:
Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Shizuoka, 422, Japan
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In the previous paper [3], we introduced new coordinates to the Schottky space, and defined the augmented Schottky spaces . Here, in § 1, we will define fiber spaces over the augmented Schottky spaces. In §2, we will consider a property of the new coordinates, namely, we will state a relation between limits of sequences of elements of the new coordinates and limits of sequences of length of loops on Riemann surfaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 73 - 78
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Bers, L., Spaces of degenerating Riemann surfaces, Ann. of Math. Studies, 79 (1974), 43–55.Google Scholar
[ 2 ] Bers, L., Automorphie forms for Schottky groups, Adv. in Math., 16 (1975), 332–361.Google Scholar
[ 3 ] Sato, H., On augmented Schottky spaces and automorphic forms, I, Nagoya Math. J., 76 (1979), 151–175.Google Scholar
[ 4 ] Sato, H., On augmented Schottky spaces and automorphic forms, II, Nagoya Math. J., 88 (1982), 79–119.Google Scholar