Sign changes of the Eisenstein series on the critical line
Junehyuk Jung, Matthew P. Young

TL;DR
This paper establishes a quantitative lower bound on the number of nodal domains of Eisenstein series on the critical line, using a novel restricted QUE theorem with shrinking test function support.
Contribution
It introduces a new quantitative restricted QUE theorem that enables analysis of nodal domains of Eisenstein series with variable support.
Findings
Proves a lower bound on nodal domains of Eisenstein series.
Develops a restricted QUE theorem with shrinking support.
Provides new insights into the structure of 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.
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