论文标题
$（4，p）$ - 算术双曲晶格，$ p \ geq 2 $，在三个方面
The $(4,p)$-arithmetic hyperbolic lattices, $p\geq 2$, in three dimensions
论文作者
论文摘要
我们确定有限的许多算术晶格$γ$在保存的等级均值$ 3 $ -Space $ \ mathbb {h}^3 $由订单$ 4 $和订单元素和订单元素$ p \ geq 2 $产生的均值$ 3美元。因此，$γ$具有$γ\ cong \ langle f，g：f^4 = g^p = w（f，g）= \ cdots = 1 \ rangle $的介绍，我们发现一定是$ p \ in \ in \ in \ in \ {2,3,4,5,6，\ infty \ iffty \} $，$ p = $ p = invariant trace field $kΓ=\mathbb{Q}(\{\tr^2(h):h\inΓ\})$ is at most $4$, and each orbifold is either a two bridge link of slope $r/s$ surgered with $(4,0)$, $(p,0)$ Dehn surgery (possibly a two bridge knot if $p=4$) or a Heckoid group with slope $ r/s $和$ w（f，g）=（w_ {r/s}）^r $，带有$ r \ in \ {1,2,3,4 \} $。我们在$ psl（2，\ mathbb {c}）$中给出一个离散的忠实表示形式，并确定关联的数字理论数据。
We identify the finitely many arithmetic lattices $Γ$ in the orientation preserving isometry group of hyperbolic $3$-space $\mathbb{H}^3$ generated by an element of order $4$ and and element of order $p\geq 2$. Thus $Γ$ has a presentation of the form $Γ\cong\langle f,g: f^4=g^p=w(f,g)=\cdots=1 \rangle$ We find that necessarily $p\in \{2,3,4,5,6,\infty\}$, where $p=\infty$ denotes that $g$ is a parabolic element, the total degree of the invariant trace field $kΓ=\mathbb{Q}(\{\tr^2(h):h\inΓ\})$ is at most $4$, and each orbifold is either a two bridge link of slope $r/s$ surgered with $(4,0)$, $(p,0)$ Dehn surgery (possibly a two bridge knot if $p=4$) or a Heckoid group with slope $r/s$ and $w(f,g)=(w_{r/s})^r$ with $r\in \{1,2,3,4\}$. We give a discrete and faithful representation in $PSL(2,\mathbb{C})$ for each group and identify the associated number theoretic data.
