{"id":{"repo_id":"columbia-diss","oai_identifier":"oai:academiccommons.columbia.edu:10.7916/D8891D2V"},"canonical_url":"https://search.dev.ndltd.org/etd/columbia-diss/oai:academiccommons.columbia.edu:10.7916/D8891D2V","repository":{"repo_id":"columbia-diss","name":"Columbia University","base_url":"https://academiccommons.columbia.edu/oai"},"display":{"title":"Singular theta lifts and near-central special values of Rankin-Selberg L-functions","abstract":"In this thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for Beilinson's conjectures on special values of L-functions.","abstract_html":"In this thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for Beilinson's conjectures on special values of L-functions.","abstract_has_math":false,"creators":["Garcia, Luis Emilio"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-24T01:44:29Z","subjects":["Mathematics","Automorphic forms","Curves, Algebraic"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.7916/D8891D2V","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Garcia, Luis Emilio"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013"]},{"key":"dc:type","label":"Dc Type","values":["Theses"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Automorphic forms","Curves, Algebraic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7916/D8891D2V"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for Beilinson's conjectures on special values of L-functions."]},{"key":"dc:title","label":"Title","values":["Singular theta lifts and near-central special values of Rankin-Selberg L-functions"]}]}],"canonical_facts":{"dc:creator":["Garcia, Luis Emilio"],"dc:date":["2013"],"dc:description":["In this thesis we study integrals of a product of two automorphic forms of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for Beilinson's conjectures on special values of L-functions."],"dc:identifier":["https://doi.org/10.7916/D8891D2V"],"dc:language":["English"],"dc:subject":["Mathematics","Automorphic forms","Curves, Algebraic"],"dc:title":["Singular theta lifts and near-central special values of Rankin-Selberg L-functions"],"dc:type":["Theses"]},"updated_at":"2026-07-24T01:44:29Z"}