Counting eigenvalues for automorphisms of Riemann surfaces

Lawrence, John; Zorzitto, Frank

doi:10.1090/S0002-9939-1978-0466529-3

Counting eigenvalues for automorphisms of Riemann surfaces
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by John Lawrence and Frank Zorzitto PDF

Proc. Amer. Math. Soc. 69 (1978), 91-94 Request permission

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.

References

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