The sup-norm problem beyond the newform

DOI10.1017/S0305004124000021arXiv2111.01893OpenAlexW3208459290MaRDI QIDQ6382011

Publication date: 2 November 2021

Abstract: In this note we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation

p i

we consider a special small

G L_{2} (m a t h b b Z_{p})

-type

V

in

p i

and proof global sup-norm bounds for an average over an orthonormal basis of

V

. We achieve a non-trivial saving when the dimension of

V

grows.

Full work available at URL: https://doi.org/10.1017/s0305004124000021

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) (p)-adic theory, local fields (11F85) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)