The LS method for the classical groups in positive characteristic and the Riemann Hypothesis
The LS method for the classical groups in positive characteristic and the Riemann Hypothesis
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正特征经典群的LS方法和黎曼猜想
DOI：
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发表时间：
2012
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通讯作者：
L. Lomelí
中科院分区：
文献类型：
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作者：
L. Lomelí
我们为一般表示乘积的$gamma$因子的扩展系统提供了一个定义
We provide a definition for an extended system of $gamma$-factors for products of generic representations
$ au$ and $pi$ of split classical groups or general linear groups over a non-archimedean local field of
characteristic $p$. We prove that our $gamma$-factors satisfy a list of axioms (under the assumption
$p
eq 2$ when both groups are classical groups) and show their uniqueness (in general). This allows us
to define extended local $L$-functions and root numbers. We then obtain automorphic $L$-functions
$L(s, au imes pi)$, where $ au$ and $pi$ are globally generic cuspidal automorphic representations
of split classical groups or general linear groups over a global function field. In addition to rationality
and the functional equation, we prove that our automorphic $L$-functions satisfy the Riemann Hypothesis.