Asymptotic Expansion for Expanding Spherical Averages in Real Rank One
arXiv preprint
- First computed and verified the special case of spherical averages of orthogonal group, then completed work on equidistribution and full asymptotic expansions for expanding sectorial averages.
- Uses representation theory, spectral decomposition, and Casimir-operator methods to make spectral contributions explicit.
Asymptotic Expansion for Expanding Spherical Averages in Finite Volume
- Extends the compact-case expansion to finite-volume quotients where cusps and continuous spectrum appear.
- Studies the contribution of Eisenstein series and residual spectrum to pointwise or locally uniform asymptotics.
Asymptotic Expansion for Expanding Horospherical Averages
- Investigates asymptotic expansions for averages over horospherical orbits and related expanding translates.
- Aims to sharpen quantitative equidistribution by replacing single error terms with explicit spectral expansions.
Asymptotic Expansion for Higher-Rank Expanding Averages
- Studies multi-parameter expanding averages along split tori in higher-rank locally symmetric spaces.
- Replaces the rank-one ODE method with regular-singular PDE systems in the positive Weyl chamber.
Asymptotic Expansion for Expanding Averages over Symmetric Subgroups
- Moves beyond maximal compact subgroup averages to expanding averages over general symmetric subgroups.
- Uses invariant differential operators and radial-part methods to seek asymptotic expansions for subgroup dynamics and counting problems.
- Studies effective equidistribution for non-closed horocycle orbits in an S-adic homogeneous-space setting.
- Includes an adelic-space version based on the thickening method.
- Connects unipotent dynamics, homogeneous spaces, and quantitative orbit-distribution problems.
