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arXiv · 2111.08797

A Thin Fundamental Set for SL(2, Z)

Hongyu He
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Abstract

Let $Γ=SL(2, \mathbb Z)$ and $G=SL(2, \mathbb R)$. Let $g=kan$ be the Iwasawa decomposition. Let $ε$ be a small positive number. In this paper, we construct a fundamental set $\mathcal F_ε$ such that the $k$-component of $ g \in \mathcal F_ε$ is within the $ε$-distance from the identity. We further prove an inequality for the $L^2$-norm of functions on $G/Γ$.

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Hongyu He. 2021-11-16. A Thin Fundamental Set for SL(2, Z). https://arxiv.org/abs/2111.08797

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