On sup-norm bounds part II: $GL(2)$ Eisenstein series

Abstract

In this paper we consider the sup-norm problem in the context of analytic Eisenstein series for $GL(2)$ over number fields. We prove a hybrid bound which is sharper than the corresponding bound for Maaß forms. Our results generalise those of Huang and Xu where the case of Eisenstein series of square-free levels over the base field $\mathbb{Q}$ had been considered.

38 pages, v3: Incorporates many comments from the excellent referee

References in corpus (5)

• Hybrid sup-norm bounds for Maass newforms of powerful level
• A note on the sup norm of Eisenstein series
• Large values of newforms on GL(2) with highly ramified central character
• On the size of p-adic Whittaker functions
• Sup-norm bounds for Eisenstein series

Cited by in corpus (1)

• Hybrid bounds for the sup-norm of automorphic forms in higher rank