English

Explicit subconvexity savings for sup-norms of cusp forms on $\mathrm{PGL}_n(\mathbb R)$

Number Theory 2019-12-18 v2

Abstract

Blomer and Maga recently proved that, if FF is an L2L^2-normalized Hecke Maass cusp form for SLn(Z)\mathrm{SL}_n(\mathbb Z), and Ω\Omega is a compact subset of PGLn(R)/POn(R)\mathrm{PGL}_n(\mathbb R)/\mathrm{PO}_n(\mathbb R), then we have FΩΩλFn(n1)/8δn\|F|_\Omega\|_\infty\ll_\Omega\lambda_F^{n(n-1)/8-\delta_n} for some δn>0\delta_n>0, where λF\lambda_F is the Laplacian eigenvalue of FF. In the present paper, we prove an explicit version of their result.

Keywords

Cite

@article{arxiv.1904.12554,
  title  = {Explicit subconvexity savings for sup-norms of cusp forms on $\mathrm{PGL}_n(\mathbb R)$},
  author = {Nate Gillman},
  journal= {arXiv preprint arXiv:1904.12554},
  year   = {2019}
}

Comments

13 pages, minor edits, to appear in Journal of Number Theory