Abstract
In this work the following theorem is proved by elementary methods. Theorem. For all congruence-subgroups of the group PSL2 \(\left( (\mathbb{O}) \right)\) the following inequality holds: λ1 ≥ −\(\frac{2}{5}\), where \(\left( (\mathbb{O}) \right)\) is the ring of all Gaussian integers.
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Arkhipov, G.I., Chubarikov, V.N. Estimate from Below of the First Eigenvalue for the Beltrami–Laplace Operator in the Three-Dimensional Space. Journal of Mathematical Sciences 114, 1397–1406 (2003). https://doi.org/10.1023/A:1022244610494
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DOI: https://doi.org/10.1023/A:1022244610494