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As an application of the method, we give explicit computations of the Rankin-Selberg integral with two Eisenstein series and a cusp form.","abstract_html":"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_has_math":false,"creators":["Chen, Cangxiong"],"institution":"University of Cambridge","degree_name":"PhD","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-22T22:24:11Z","subjects":["Algebraic number theory","Automorphic forms","Asai's function","Eisenstein series","Kronecker Limit Formula","L-functions","Rankin-Selberg integral"],"languages":["en"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.53187","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Chen, Cangxiong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2015"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/306109"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic number theory","Automorphic forms","Asai's function","Eisenstein series","Kronecker Limit Formula","L-functions","Rankin-Selberg integral"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.53187"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1811fea1-ed99-4ba7-82b7-9ecb5d552c8f/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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. 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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."],"dc:format.checksum.md5":["87eda9de84448d1f82354d60eee3eb5f","01c8d6dc3ac89205a017ab77f6f90c8e"],"dc:identifier.doi":["10.17863/CAM.53187"],"dc:identifier.uri":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1811fea1-ed99-4ba7-82b7-9ecb5d552c8f/download"],"dc:language":["en"],"dc:publisher.institution":["University of Cambridge"],"dc:relation.isreferencedby.uri":["https://www.repository.cam.ac.uk/handle/1810/306109"],"dc:rights":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/462d53c4-e3cc-4051-9a18-5a6ef8b3e81d/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"dc:subject":["Algebraic number theory","Automorphic forms","Asai's function","Eisenstein series","Kronecker Limit Formula","L-functions","Rankin-Selberg integral"],"dc:title":["ON ASAI’S FUNCTION ANALOGOUS TO log |η(z)|"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:24:11Z"}