Correction to: Equidistribution of Eisenstein Series in the Level Aspect
Ikuya Kaneko, Shin-ya Koyama
TL;DR
This paper corrects and clarifies previous results on the equidistribution of Eisenstein series in the level aspect, addressing errors and refining proofs in the context of quantum unique ergodicity.
Contribution
It provides necessary corrections and modifications to earlier proofs regarding the equidistribution of Eisenstein series, ensuring mathematical accuracy.
Findings
Corrected proofs of key theorems
Refined computation of Maass cusp form contributions
Clarified mathematical and notational issues
Abstract
The second author formulated quantum unique ergodicity for Eisenstein series in the prime level aspect in "Equidistribution of Eisenstein series in the level aspect", Commun. Math. Phys. 289(3), 1131-1150 (2009). We point out errors and correct the proofs with partially weakened claims. This article of corrigendum and addendum comprises three sections. Section 1 is devoted to making concise corrections to the claim and the proof of Theorems 1.2 and 1.3, and Sect. 2 serves as a modification of the computation of the contribution from Maass cusp forms. Other relatively marginal mathematical issues and notational/typographical errors are listed afterwards in Sect. 3.
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