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- W4300884562 abstract "We prove three main results: all Langlands-Shahidi automorphic $L$-functions over function fields are rational; after twists by highly ramified characters our automorphic $L$-functions become polynomials; and, if $pi$ is a globally generic cuspidal automorphic representation of a split classical group or a unitary group ${bf G}_n$ and $tau$ a cuspidal (unitary) automorphic representation of a general linear group, then $L(s,pi times tau)$ is holomorphic for $Re(s) > 1$ and has at most a simple pole at $s=1$. We also prove the holomorphy and non-vanishing of automorphic exterior square, symmetric square and Asai L-functions for $Re(s) > 1$. Finally, we complete previous results on functoriality for the classical groups over function fields." @default.
- W4300884562 created "2022-10-04" @default.
- W4300884562 creator A5041207585 @default.
- W4300884562 date "2015-05-22" @default.
- W4300884562 modified "2023-10-16" @default.
- W4300884562 title "On the rationality and holomorphy of Langlands-Shahidi L-functions over function fields" @default.
- W4300884562 doi "https://doi.org/10.48550/arxiv.1505.06043" @default.
- W4300884562 hasPublicationYear "2015" @default.
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