Asymptotics of degenerating Eisenstein series

TL;DR

This paper investigates the asymptotic behavior of degenerating Eisenstein series on punctured Riemann surfaces, motivated by questions about the $L_{2}$-cohomology of the Takhtajan-Zograf metric.

Contribution

It provides estimates for the asymptotic orders of Eisenstein series during surface degeneration, addressing a question posed by To and Weng.

Findings

Estimates for asymptotic orders of Eisenstein series

Insights into $L_{2}$-cohomology of Takhtajan-Zograf metric

Connections between degenerating surfaces and Eisenstein series

Abstract

We give some estimates for the asymptotic orders of degenerating Eisenstein series for some families of degenerating punctured Riemann surfaces, which is motivated by the question identifying $L_{2}$-cohomology of the Takhtajan-Zograf metric that is originally asked by To and Weng.