ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|

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.

Name dc:type.qualificationname

PhD

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2015

Author dc:creator

• Chen, Cangxiong

• Algebraic number theory
• Automorphic forms
• Asai's function
• Eisenstein series
• Kronecker Limit Formula
• L-functions
• Rankin-Selberg integral

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.53187

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/306109