Applications of analytic newvectors for $$\mathrm {GL}(n)$$
نویسندگان
چکیده
We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment central $L$-values as strong Lindel\"of on average. also random matrix prediction about distribution low-lying zeros $L$-function The new ideas proofs include use newvectors construct approximate projector spectrum bounded conductors soft local (both at finite infinite places) analysis geometric side Kuznetsov trace formula.
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2021
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-021-02207-5