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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A $p$-adic analogue of the Gauss-Bonnet theorem for certain Mumford curves
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by Richard M. Freije PDF
Proc. Amer. Math. Soc. 107 (1989), 323-332 Request permission


If $K$ is a local field, $L$ a quadratic extension, $\Gamma$ a Schottky group co-compact in ${\text {PG}}{{\text {L}}_2}(K)$ then the quotient $L - K/\Gamma$ corresponds to the $L$-points of a Mumford curve. In this paper we calculate $\int _{L - K/\Gamma } {d\mathcal {M}}$ where $\mathcal {M}$ is an ${\text {PG}}{{\text {L}}_2}(K)$ invariant measure on $L - K$, in terms of the genus of the corresponding curve.
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  • Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504, DOI 10.1007/978-3-642-61856-7
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 323-332
  • MSC: Primary 11G20; Secondary 14G20
  • DOI:
  • MathSciNet review: 972230