Hybrid subconvexity bounds for L (\tfrac12, Sym² f ⊗ g)

2014/01/26 by Roman Holowinsky, Holowinsky, Roman, Ritabrata Munshi +3
Mathematics · #11M99 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M99

paper · pdf · doi:10.48550/arxiv.1401.6695

1st draft, 27 pages

arxiv created 2014/01/26 · arxiv updated 2014/01/28

Abstract

Fix an integer κ\geqslant 2. Let P be prime and let k> κ be an even integer. For f a holomorphic cusp form of weight k and full level and g a primitive holomorphic cusp form of weight 2 κ and level P, we prove hybrid subconvexity bounds for L (\tfrac12, Sym² f ⊗ g) in the k and P aspects when P^\frac 13 64 + δ < k < P^{\frac 3 8 - δ} for any 0 < δ< \frac 11 128. These bounds are achieved through a first moment method (with amplification when P^\frac 13 64 < k \leqslant P^\frac 4 13).

Related

• Hybrid Subconvexity Bound for L((1)/(2),Sym² f⊗ρ) via the Delta Method
• The Second Moment of Rankin-Selberg L-function and Hybrid Subconvexity Bound
• Hybrid Level Aspect Subconvexity for GL(2)\× GL(1) Rankin-Selberg\n L-Functions
• Subconvexity for Symmetric Square L-functions off-centre
• Hybrid subconvexity bounds for twists of \rm GL(3) L-functions