非阿基米德发展在扭曲 $L$-函数的阿基米德非零结果中的应用
Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$-functions
AI总结：
本文通过结合伊万萨瓦理论中的非阿基米德方法与新机制，证明了特定无限族中除有限个酉特征外所有扭曲的某类自守 $L$-函数的扭曲中心临界值非零。
摘要：
我们证明了对于特定无限族中除有限个酉特征外的所有扭曲，某类自守 $L$-函数的扭曲中心临界值非零。虽然本文关注与酉群上某些自守表示相关的 $L$-函数，但它展示了如何将伊万萨瓦理论中数十年的非阿基米德方法与新机制的输出相结合，以获得更广泛的非零结果。在涉及中间步骤的附录中，我们还概述了如何将酉群上 $p$-adic Eisenstein 级数和 $L$-函数的相关先前计算扩展到仅需 $p$ 在相关反射域中非分歧的情形（而先前的构造要求 $p$ 完全分裂）。
英文摘要：
We prove the nonvanishing of the twisted central critical values of a class of automorphic $L$-functions for twists by all but finitely many unitary characters in particular infinite families. While this paper focuses on $L$-functions associated to certain automorphic representations of unitary groups, it illustrates how decades-old nonarchimedean methods from Iwasawa theory can be combined with the output of new machinery to achieve broader nonvanishing results. In an appendix, which concerns an intermediate step, we also outline how to extend relevant prior computations for $p$-adic Eisenstein series and $L$-functions on unitary groups to the case where primes dividing $p$ merely needs to be unramified (whereas prior constructions required $p$ to split completely) in the associated reflex field.
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。
