{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/139475"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/139475","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions","abstract":"A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the function field case by Yun and Zhang which showed that higher derivatives of the base change L-function of an unramified automorphic representation over PGL₂ over a function field are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for an anisotropic torus. We prove in the function field case that the higher derivatives of the square of the L-function of unramified automorphic representations over PGL₂ are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for the split torus.","abstract_html":"A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the function field case by Yun and Zhang which showed that higher derivatives of the base change L-function of an unramified automorphic representation over PGL₂ over a function field are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for an anisotropic torus. We prove in the function field case that the higher derivatives of the square of the L-function of unramified automorphic representations over PGL₂ are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for the split torus.","abstract_has_math":false,"creators":["Chen, Yongyi"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Mathematics","school":null,"contributors":[],"advisors":["Wei Zhang"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-06","date_published":"2021-06","updated_at":"2026-07-22T22:22:04Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"rights_urls":["http://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/139475","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Wei Zhang"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Mathematics"]},{"key":"dc:creator","label":"Author","values":["Chen, Yongyi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-01-14T15:13:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-01-14T15:13:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-06"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctoral","Doctor of Philosophy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright - Educational Use Permitted","Copyright MIT"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/page/InC-EDU/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1721.1/139475"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the function field case by Yun and Zhang which showed that higher derivatives of the base change L-function of an unramified automorphic representation over PGL₂ over a function field are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for an anisotropic torus. We prove in the function field case that the higher derivatives of the square of the L-function of unramified automorphic representations over PGL₂ are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for the split torus."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wei Zhang"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Mathematics"],"dc:creator":["Chen, Yongyi"],"dc:date.accessioned":["2022-01-14T15:13:36Z"],"dc:date.available":["2022-01-14T15:13:36Z"],"dc:date.issued":["2021-06"],"dc:description.abstract":["A rising philosophy in the theory of automorphic representations in number theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an elliptic curve is equal, up to a constant, to the Néron-Tate height pairing of a special point called a Heegner point on the elliptic curve. A more recent result was proven in the function field case by Yun and Zhang which showed that higher derivatives of the base change L-function of an unramified automorphic representation over PGL₂ over a function field are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for an anisotropic torus. We prove in the function field case that the higher derivatives of the square of the L-function of unramified automorphic representations over PGL₂ are equal, up to a constant, to the self-intersection number, inside the moduli stack of PGL₂-shtukas, of the moduli stack of shtukas for the split torus."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/139475"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:22:04Z"}