Mathematics – Number Theory
Scientific paper
2002-10-16
Mathematics
Number Theory
8 pages
Scientific paper
We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\pi$ be a unitary, cuspidal, automorphic representation of $GL_n(\A_K)$. Let $S$ be a set of finite places of $K$, such that the sum $\sum_{v\in S}Nv^{-2/(n^2+1)}$ is convergent. Then $\pi$ is uniquely determined by the collection of the local components $\{\pi_v\mid v\not\in S, ~v \~\text{finite}\}$ of $\pi$. Combining this theorem with base change, it is possible to consider sets $S$ of positive density, having appropriate splitting behavior with respect to solvable extensions of $K$, and where $\pi$ is determined upto twisting by a character of the Galois group of $L$ over $K$.
No associations
LandOfFree
On strong multiplicity one for automorphic representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On strong multiplicity one for automorphic representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On strong multiplicity one for automorphic representations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-569581