Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions

@article{Shin2012SatoTateTF,
title={Sato–Tate theorem for families and low-lying zeros of automorphic \$\$L\$\$L-functions},
author={Sug Woo Shin and Nicolas Templier},
journal={Inventiones mathematicae},
year={2012},
volume={203},
pages={1-177}
}
• Published 9 August 2012
• Mathematics
• Inventiones mathematicae
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $$G$$G be a reductive group over a number field $$F$$F which admits discrete series representations at infinity. Let $$^{L}G=\widehat{G} \rtimes \mathrm{Gal}(\bar{F}/F)$$LG=G^⋊Gal(F¯/F) be the associated $$L$$L-group and $$r:{}^L G\rightarrow \mathrm{GL}(d,\mathbb {C})$$r:LG→GL(d,C) a continuous homomorphism which is irreducible and does not factor through…
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