本原长度谱中的等差数列
Arithmetic Progressions in the Primitive Length Spectrum
摘要：
本文证明了不含欧几里德因子或紧因子的经典型算术局部对称轨道褶在其本原长度谱中具有任意长的等差数列.此外，我们还证明了每个本原长度在其本原长度谱中出现在任意长的等差数列中的更强性质。这证实了一个方向的猜想拉丰-麦克雷诺兹，其中指出，财产的每一个原始长度发生在任意长的等差数列的特点算术等空间。
英文摘要：
In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in its primitive length spectrum. Moreover, we show the stronger property that every primitive length occurs in arbitrarily long arithmetic progressions in its primitive length spectrum. This confirms one direction of a conjecture of Lafont--McReynolds, which states that the property of having every primitive length occur in arbitrarily long arithmetic progressions characterizes the arithmeticity of such spaces.
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