Arithmetic Progressions in the Primitive Length Spectrum
Arithmetic Progressions in the Primitive Length Spectrum
复制标题
本原长度谱的算术级数
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
N. Miller
中科院分区：
文献类型：
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作者：
N. Miller
本文证明了不含欧几里得或紧因子的经典局部对称算术分支在其原始长度谱上有任意长的算术级数。此外，我们还证明了更强的性质，即每个本原长度在其本原长谱中以任意长的算术级数出现。这证实了Lafont-McReynolds猜想的一个方向，即每个本原长度都出现在任意长的算术级数中的性质刻画了这种空间的算术性。
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.
影响因子：
1
作者：
Gorodnik A
通讯作者：
Gorodnik A