Subconvexity for $L$-functions of non-spherical cusp forms on ${\rm GL}(3)$
Tom 192 / 2020
Acta Arithmetica 192 (2020), 31-62
MSC: Primary 11M41, 11F55, 11F72.
DOI: 10.4064/aa180125-5-2
Opublikowany online: 24 October 2019
Streszczenie
Let $f$ be a cusp form for ${\rm SL}(3, \Bbb {Z})$ associated with a generalized principal series representation of minimal weight $d$, spectral parameter $r$ and associated $L$-function $L(s, f)$. For $r \asymp d \asymp T$ the subconvexity bound $L(1/2, f) \ll T^{3/4 - 1/140000 }$ is proved.
