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ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)| 10.17863/CAM.53187 Chen, Cangxiong 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. University of Cambridge 2015 Thesis doctoral PhD en https://www.repository.cam.ac.uk/handle/1810/306109 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download 87eda9de84448d1f82354d60eee3eb5f https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1811fea1-ed99-4ba7-82b7-9ecb5d552c8f/download 01c8d6dc3ac89205a017ab77f6f90c8e https://www.rioxx.net/licenses/all-rights-reserved/ Algebraic number theory Automorphic forms Asai's function Eisenstein series Kronecker Limit Formula L-functions Rankin-Selberg integral