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Linear diophantine equations with cyclic coefficient matrices and its applications to Riemann surfaces

Published online by Cambridge University Press:  20 January 2009

Nobumasa Takigawa
Nobumasa Takigawa
Affiliation:
Department of Applied Mathematics, Okayama University of Science, Ridai-cho, Okayama, 700, Japan
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Let co, c1, …, cn-1 be the nonzero complex numbers and let C = (cu+1,v+1) = (cn+u-v), O≦u,v≦n — 1, be a cyclic matrix, where n + u — v is taken modulo n. In this paper we shall give the solution of the linear equations

where Lu (0≦u≦n —1) is a fixed complex number. In Theorem 1 weshall give a necessary and sufficient condition for (1) to have an integral solution.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 3 , October 1985 , pp. 369 - 380
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

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