Subconvexity bound for L-functions: t-aspect
Tom 194 / 2020
Acta Arithmetica 194 (2020), 111-133
MSC: Primary 11F66, 11M41; Secondary 11F55.
DOI: 10.4064/aa180711-9-5
Opublikowany online: 2 March 2020
Streszczenie
Let F be a holomorphic Hecke eigenform or a Hecke–Maass cusp form for the full modular group {\rm SL}(2, \mathbb {Z}). We use the circle method to prove the Weyl exponent for {\rm GL}(2) L-functions. We show that L ( {1}/{2} + it, F ) \ll _{F, \epsilon } ( 2 + |t| )^{1/3 + \epsilon } for any \epsilon \gt 0.
