区分有限群特征标和精化局部-整体现象
Distinguishing finite group characters and refined local-global phenomena
摘要：
塞尔获得了一个尖锐的界限如何经常两个不可约度$n$复杂字符的有限群可以同意，这告诉我们有多少当地的因素决定了阿廷$L$ -功能。我们考虑更微妙的问题，找到一个尖锐的界限时，这些对象是原始的，并回答这些问题的$n=2,3$。这为GL $(n)$的自守表示提供了一些关于精细强重数1现象的见解。对于一般的$n$，我们还回答了PSL $(2,q)$和SL $(2,q)$族的特征问题。
英文摘要：
Serre obtained a sharp bound on how often two irreducible degree $n$ complex characters of a finite group can agree, which tells us how many local factors determine an Artin $L$-function. We consider the more delicate question of finding a sharp bound when these objects are primitive, and answer these questions for $n=2,3$. This provides some insight on refined strong multiplicity one phenomena for automorphic representations of GL$(n)$. For general $n$, we also answer the character question for the families PSL$(2,q)$ and SL$(2,q)$.
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。
