On the subconvexity problem for L-functions on GL(3)

Abstract

Let f be a cusp form for the group SL(3, Z) with Langlands parameter mu and associated L-function L(s, f). If mu is in generic position, i.e. away from the Weyl chamber walls and away from the self-dual forms, we prove the subconvexity bound L(1/2, f) << || mu || ^{3/4 - 1/120000}.

46 pages

References in corpus (2)

• The subconvexity problem for $\GL_{2}$
• On Sums of SL(3,Z) Kloosterman Sums

Cited by in corpus (10)

• Bounds for twists of $\mathrm{GL}(3)$ $L$-functions
• The arithmetic Kuznetsov formula on $GL(3)$, II: The general case
• On the global sup-norm of GL(3) cusp forms
• Bilinear forms with $G{L}_3$ Kloosterman sums and the spectral large sieve
• Subconvexity for L-functions of non-spherical cusp forms on GL(3)
• Subconvexity for $GL(3)\times GL(2)$ $L$-functions in $GL(3)$ spectral aspect
• Subconvexity for twisted $L$-functions on ${\mathrm{GL}}_3$ over the Gaussian number field
• Central Values of $GL(2)\times GL(3)$ Rankin-Selberg $L$-functions with Applications
• Mollification and non-vanishing of automorphic $L$-functions on GL(3)
• Spectral summation formula for GSp(4) and moments of spinor L-functions