Gamma因子根数和区分
Gamma factors root numbers and distinction
摘要：
研究了$p$ -adic域的二次扩张上一般线性群表示的局部不变量的区别与特殊值之间的关系。我们表明，当地的Rankin-Selberg根数的任何一对杰出的表示是平凡的，作为一个推论，我们得到一个模拟的全球根数的任何一对杰出的尖形表示。我们进一步研究在$1/2$的伽玛因子是平凡的区别表示以及逆问题的程度。
英文摘要：
We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of $p$-adic fields. We show that the local Rankin-Selberg root number of any pair of distinguished representation is trivial and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at $1/2$ is trivial for distinguished representations as well as the converse problem.
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。
