ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|
type: CreativeWork
description: Kronecker’s first limit formula describes the constant term in the Laurent expansion of a non-holomorphic Eisenstein series at one of its poles. Asai generalised the limit formula to Eisenstein series of level one defined for a number field with class number one and obtained a function analogous to the logarithm of the absolute value of the eta function. In this thesis we reformulate Asai’s function adelically using the theory of admissible representations for GL2 and simultaneously remove the restriction on class number and level. As an application of the method, we give explicit computations of the Rankin-Selberg integral with two Eisenstein series and a cusp form.
abstract: Kronecker’s first limit formula describes the constant term in the Laurent expansion of a non-holomorphic Eisenstein series at one of its poles. Asai generalised the limit formula to Eisenstein series of level one defined for a number field with class number one and obtained a function analogous to the logarithm of the absolute value of the eta function. In this thesis we reformulate Asai’s function adelically using the theory of admissible representations for GL2 and simultaneously remove the restriction on class number and level. As an application of the method, we give explicit computations of the Rankin-Selberg integral with two Eisenstein series and a cusp form.
author: Chen, Cangxiong
language: en
keywords: Algebraic number theory, Automorphic forms, Asai's function, Eisenstein series, Kronecker Limit Formula, L-functions, Rankin-Selberg integral
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2015
date modified: 2026-07-22T22:24:11Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.53187