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A reduction point algorithm for cocompact Fuchsian groups and applications. (English) Zbl 1359.94874

Summary: In the present article we propose a reduction point algorithm for any Fuchsian group in the absence of parabolic transformations. We extend to this setting classical algorithms for Fuchsian groups with parabolic transformations, such as the flip flop algorithm known for the modular group \(\mathrm{SL}(2,\mathbb{Z})\) and whose roots go back to [J.-P. Serre, A course in arithmetic. New York etc.: Springer-Verlag (1973; Zbl 0256.12001)]. The research has been partially motivated by the need to design more efficient codes for wireless transmission data and for the study of Maass waveforms under a computational point of view.

MSC:

94B40 Arithmetic codes
11Y16 Number-theoretic algorithms; complexity
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
65Y04 Numerical algorithms for computer arithmetic, etc.

Citations:

Zbl 0256.12001
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Full Text: DOI

References:

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