Deformations of Theta Integrals and A Conjecture of Gross-Zagier
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001397/type/journal_article |
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| author | Jan H. Bruinier Yingkun Li Tonghai Yang |
| author_facet | Jan H. Bruinier Yingkun Li Tonghai Yang |
| author_sort | Jan H. Bruinier |
| collection | DOAJ |
| description | In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed as the Doi-Naganuma theta lift of a deformed theta integral on hyperbolic 1-space. |
| format | Article |
| id | doaj-art-7f1415d11b344c2a8ee4be5211d5ca2c |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-7f1415d11b344c2a8ee4be5211d5ca2c2025-08-20T02:57:07ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2024.139Deformations of Theta Integrals and A Conjecture of Gross-ZagierJan H. Bruinier0https://orcid.org/0000-0002-1653-8230Yingkun Li1https://orcid.org/0000-0002-3974-1389Tonghai Yang2Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, Darmstadt, D–64289, Germany; E-mail:Max Planck Institute for Mathematics, Vivatsgasse 7, Bonn, D–53111, Germany; E-mail:Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Dr., Madison, WI 53706, USA;In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over a real quadratic field, which is constructed as the Doi-Naganuma theta lift of a deformed theta integral on hyperbolic 1-space.https://www.cambridge.org/core/product/identifier/S2050509424001397/type/journal_article11F3711F4111G15 |
| spellingShingle | Jan H. Bruinier Yingkun Li Tonghai Yang Deformations of Theta Integrals and A Conjecture of Gross-Zagier Forum of Mathematics, Sigma 11F37 11F41 11G15 |
| title | Deformations of Theta Integrals and A Conjecture of Gross-Zagier |
| title_full | Deformations of Theta Integrals and A Conjecture of Gross-Zagier |
| title_fullStr | Deformations of Theta Integrals and A Conjecture of Gross-Zagier |
| title_full_unstemmed | Deformations of Theta Integrals and A Conjecture of Gross-Zagier |
| title_short | Deformations of Theta Integrals and A Conjecture of Gross-Zagier |
| title_sort | deformations of theta integrals and a conjecture of gross zagier |
| topic | 11F37 11F41 11G15 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001397/type/journal_article |
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