Sign changes of the Eisenstein series on the critical line

Abstract

We prove a quantitative lower bound on the number of nodal domains of the real-analytic Eisenstein series. The main tool in the proof is a quantitative restricted QUE theorem where the support of the test function is allowed to shrink with the Laplace eigenvalue.

19 pages

References in corpus (4)

• Distribution of mass of holomorphic cusp forms
• Nodal domains of Maass forms I
• The quantum unique ergodicity conjecture for thin sets
• Quantum ergodicity for restrictions to hypersurfaces