The subconvexity problem for GL2

2009/03/31 by Philippe Michel, Akshay Venkatesh · 261 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Feature (linguistics) #Field (mathematics) #Linguistics #Mathematics #Philosophy #Pure mathematics #math.NT #msc:11F66 #msc:11F70

paper · pdf · doi:10.1007/s10240-010-0025-8

published in Publications mathématiques de l IHÉS 111, 171-271 (Springer Nature) · Almost final version to appear in Publ. Math IHES. References updated.

arxiv created 2010/03/09 · openalex publication_date 2010/05/18 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL 1 and GL 2 automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino–Ikeda.

Citations

• Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory
• A Functional Equation for the Spectral Fourth Moment of Modular Hecke L-Functions
• Coefficients of Maass Forms and the Siegel Zero
• Démonstration de la conjecture τ
• Sparse equidistribution problems, period bounds, and subconvexity
• On the generalized Ramanujan conjecture for GL(h)

Cited by

• Hybrid subconvexity bounds for twisted L-functions on GL(3)
• Gaps between zeros of GL(2) L-functions
• Automorphic SL₂-periods and the subconvexity problem for GL₂ × GL₃
• Microlocal lifts and quantum unique ergodicity on GL2(ℚp)
• Large Values of Newforms on GL(2) with Highly Ramified Central Character
• Lindelöf hypothesis [wikipedia]

Related

• Automorphic SL₂-periods and the subconvexity problem for GL₂ × GL₃
• The subconvexity bound for standard L-function in level aspect
• Subconvexity for L-Functions on GL₃ over Number Fields
• Subconvexity bounds in depth-aspect for automorphic L-functions on GL(2)
• Periods, subconvexity of L-functions and representation theory