A note on the sup norm of Eisenstein series

Abstract

We prove a sup norm bound on the real-analytic Eisenstein series, of the form $E(z,1/2+iT)\ll T^{3/8+\epsilon }$, uniformly for $z$ in a fixed compact subset of $\mathbb{H}$.

9 pages. v2: improved exposition

References in corpus (1)

• Subconvexity for sup-norms of automorphic forms on PGL(n)

Cited by in corpus (4)

• On sup-norm bounds part II: $GL(2)$ Eisenstein series
• Sup-norm and nodal domains of dihedral Maass forms
• Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity
• On the growth of Rankin-Selberg L-functions for $SL(2)$