一个次凸度量覆盖素数测地线定理与志村对应
A Subconvex Metaplectic Prime Geodesic Theorem and the Shimura Correspondence
AI总结：
该论文证明了素数测地线定理的次凸误差界，并首次为最优指数1+ε提供理论证据，通过利用主项与最大剩余拉普拉斯特征值的关系。
摘要：
我们研究了在算术背景下，误差项依赖于可变权重及其更高度量覆盖的素数测地线定理，尽管我们的输入是软的，但每个都允许次凸改进。前者打破了Hejhal（1983）在乘子系统非平凡时的3/4屏障，而后者代表了支持关于最优指数1+ε的普遍共识的第一个理论证据，当乘子系统特化为久保田特征时。我们的论证依赖于一个优雅的现象：素数测地线定理中的主项由最大的剩余拉普拉斯特征值的大小控制，从而相对于其乘子系统平凡的志村对应，在误差项中同时实现多项式幂节省。
英文摘要：
We investigate the prime geodesic theorem with an error term dependent on the varying weight and its higher metaplectic coverings in the arithmetic setting, each admitting subconvex refinements despite the softness of our input. The former breaks the $\frac{3}{4}$-barrier due to Hejhal (1983) when the multiplier system is nontrivial, while the latter represents the first theoretical evidence supporting the prevailing consensus on the optimal exponent $1+\varepsilon$ when the multiplier system specialises to the Kubota character. Our argument relies on the elegant phenomenon that the main term in the prime geodesic theorem is governed by the size of the largest residual Laplace eigenvalue, thereby yielding a simultaneous polynomial power-saving in the error term relative to its Shimura correspondent where the multiplier system is trivial.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
