On sup-norms of cusp forms of powerful level

Abstract

Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and Laplace eigenvalue λ. It is shown that |f|_\infty <<_{λ, ε} N^{-1/12 + ε} for any ε>0. The exponent is further improved in the case when N is not divisible by "small squares". Our work extends and generalizes previously known results in the special case of N squarefree.

Final version, to appear in JEMS. Please also note that the results of this paper have been significantly improved in my recent paper arXiv:1509.07489 which uses a fairly different methodology

References in corpus (2)

• Hybrid sup-norm bounds for Maass newforms of powerful level
• Large values of cusp forms on GL(n)

Cited by in corpus (6)

• Hybrid sup-norm bounds for Maass newforms of powerful level
• Bounds for eigenforms on arithmetic hyperbolic 3-manifolds
• On the order of vanishing of newforms at cusps
• Subconvexity for Half Integral Weight $L$-functions
• Supnorm of Modular Forms of half-integral Weight in the Weight Aspect
• The sup-norm problem for PGL(4)