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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Counting eigenvalues for automorphisms of Riemann surfaces

Authors: John Lawrence and Frank Zorzitto
Journal: Proc. Amer. Math. Soc. 69 (1978), 91-94
MSC: Primary 30A46; Secondary 14H35
MathSciNet review: 0466529
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Abstract: Let n be a prime, A, B, C disjoint sets, $ f:{Z_n} \to A \cup B \cup C$ be such that $ f(\bar x) \in A$ iff $ f( - \bar x) \in C$ and $ f(\bar x + \bar y) \notin C$ whenever $ f(\bar x),f(\bar y) \in A$. Then the cardinality of $ {f^{ - 1}}[B]$ tends to infinity with n. Using this, certain eigenvalues for automorphisms of the Riemann surfaces defined by the equation $ {y^n} = {x^{{m_1}}}{(x - 1)^{{m_2}}}{(x - z)^{{m_3}}}$ are counted.

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Keywords: Riemann surface, automorphism, differentials, eigenvalues
Article copyright: © Copyright 1978 American Mathematical Society

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