Lattice points counting and bounds on periods of maass forms

Andre Reznikov, Feng Su

Research output: Contribution to journalArticlepeer-review


We provide a “soft” proof for nontrivial bounds on spherical, hyperbolic, and unipotent Fourier coefficients of a fixed Maass form for a general cofinite lattice Γ in PGL2(R). We use the amplification method based on the Airy type phenomenon for corresponding matrix coefficients and an effective Selberg type pointwise asymptotic for the lattice points counting in various homogeneous spaces for the group PGL2(R). This requires only L2-theory. We also show how to use the uniform bound for the L4-norm of K-types in a fixed automorphic representation of PGL2(R) in order to slightly improve these bounds.

Original languageEnglish
Pages (from-to)2073-2102
Number of pages30
JournalTransactions of the American Mathematical Society
Issue number3
Publication statusPublished - 1 Aug 2019


  • And phrases
  • Automorphic representations
  • Periods
  • Subconvexity bounds for L-functions

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