切博塔廖夫测地定理：非分裂情形
Chebotarev geodesic theorem: non-split case
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中文总结 AI 辅助
该研究针对不定四元数序的同余子群，将素测地定理问题归约为已解决的分裂情形，证明其切博塔廖夫密度定理测地类似式的指数为$25/36 + \boldsymbol{\u03B5}$，并推广至所有$\boldsymbol{\u005Cmathbb{Q}}$上的此类同余子群。
中文摘要 AI 辅助
我们研究不定四元数序的同余子群的素测地定理，证明这类群对应的切博塔廖夫密度定理的测地类似式成立，指数为$25/36 + \boldsymbol{\u03B5}$。特别地，我们由此推得，对$\boldsymbol{\u005Cmathbb{Q}}$上任意不定四元数序的任意同余子群，素测地定理成立的指数为$25/36 + \boldsymbol{\u03B5}$。证明思路是将问题归约为分裂情形，该情形已由作者此前处理完成。
英文摘要
We study the prime geodesic theorem for congruence subgroups of indefinite quaternion orders. We prove that the geodesic analogue of the Chebotarev density theorem for these groups holds with exponent $25/36 + \varepsilon$. In particular, we deduce that the prime geodesic theorem holds with exponent $25/36 + \varepsilon$ for any congruence subgroup of any indefinite quaternion order over $\mathbb{Q}$. The idea of the proof is to reduce the problem to the split case, which has been handled previously by the author.
