Journal article
Hypothesis H and the prime number theorem for automorphic representations
Functiones et Approximatio Commentarii Mathematici, Vol.37(2), pp.461-471
2007
DOI: 10.7169/facm/1229619665
Abstract
For any unitary cuspidal representations $\pi_n$ of $GL_n(\Q_\A)$, $n=2,3,4$, respectively, consider two automorphic representations $\Pi$ and $\Pi'$ of $GL_6(\Q_\A)$, where $\Pi_p\cong\wedge^2\pi_{4,p}$ for $p\neq 2,3$ and $\pi_{4,p}$ not supercuspidal, and $\Pi'=\pi_2\boxtimes\pi_3$. First, Hypothesis H for $\Pi$ and $\Pi'$ is proved. Then contributions from prime powers are removed from the prime number theorem for cuspidal representations $\pi$ and $\pi'$ of $GL_m(\Q_\A)$ and $GL_{m'}(\Q_\A)$, respectively. The resulting prime number theorem is unconditional when $m,m'\leq 4$ and is under Hypothesis H otherwise.
Details
- Title: Subtitle
- Hypothesis H and the prime number theorem for automorphic representations
- Creators
- Jie Wu - AnalyseYangbo Ye - Department of Mathematics
- Contributors
- Jie Wu (Editor)
- Resource Type
- Journal article
- Publication Details
- Functiones et Approximatio Commentarii Mathematici, Vol.37(2), pp.461-471
- Publisher
- Poznań : Wydawnictwo Naukowe Uniwersytet im. Adama Mickiewicza
- DOI
- 10.7169/facm/1229619665
- ISSN
- 0208-6573
- eISSN
- 2080-9433
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985879702771
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