Computing Special L-Values of Certain Modular Forms with Complex Multiplication
In this expository paper, we illustrate two explicit methods that lead to special L-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of L-functions obtained from Calabi-Yau manifolds defined over Q.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209760 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Computing Special L-Values of Certain Modular Forms with Complex Multiplication / W.-C.W. Li, L. Long, F.-T. Tu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 45 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-209760 |
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Li, W.-C.W. Long, L. Tu, F.-T. 2025-11-26T11:22:14Z 2018 Computing Special L-Values of Certain Modular Forms with Complex Multiplication / W.-C.W. Li, L. Long, F.-T. Tu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 45 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 11F11; 11F67; 11M36; 33C05 arXiv: 1803.06072 https://nasplib.isofts.kiev.ua/handle/123456789/209760 https://doi.org/10.3842/SIGMA.2018.090 In this expository paper, we illustrate two explicit methods that lead to special L-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of L-functions obtained from Calabi-Yau manifolds defined over Q. The research of Li is partially supported by Simons Foundation grant # 355798, Long by NSF grant DMS #1602047, and Tu by the AWM-NSF Mentoring Travel Grant, which supported her visit to Pennsylvania State University to work with Li in 2017 and 2018. The authors would like to thank the anonymous referees, Jerome W. Hoffman, Ming-Lun Hsieh, Ye Tian, Yifan Yang, and Wadim Zudilin for their helpful comments and feedback. At the early stage of this work, the authors benefited from their visits to the Institute of Mathematical Research at the University of Hong Kong in the summer of 2017. To IMR, they express their gratitude for its hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Computing Special L-Values of Certain Modular Forms with Complex Multiplication Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication |
| spellingShingle |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication Li, W.-C.W. Long, L. Tu, F.-T. |
| title_short |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication |
| title_full |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication |
| title_fullStr |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication |
| title_full_unstemmed |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication |
| title_sort |
computing special l-values of certain modular forms with complex multiplication |
| author |
Li, W.-C.W. Long, L. Tu, F.-T. |
| author_facet |
Li, W.-C.W. Long, L. Tu, F.-T. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In this expository paper, we illustrate two explicit methods that lead to special L-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of L-functions obtained from Calabi-Yau manifolds defined over Q.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209760 |
| citation_txt |
Computing Special L-Values of Certain Modular Forms with Complex Multiplication / W.-C.W. Li, L. Long, F.-T. Tu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 45 назв. — англ. |
| work_keys_str_mv |
AT liwcw computingspeciallvaluesofcertainmodularformswithcomplexmultiplication AT longl computingspeciallvaluesofcertainmodularformswithcomplexmultiplication AT tuft computingspeciallvaluesofcertainmodularformswithcomplexmultiplication |
| first_indexed |
2025-12-07T21:09:13Z |
| last_indexed |
2025-12-07T21:09:13Z |
| _version_ |
1850886169266487296 |