Difference Equation for Quintic 3-Fold
In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type of -difference equations at = 0 and = ∞. We consider two special cases; the first is the -difference equation of the -theoretic -function of the quintic, which is degree 25; we use Adams' method to fin...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211625 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Difference Equation for Quintic 3-Fold. Yaoxinog Wen. SIGMA 18 (2022), 043, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862690023723237376 |
|---|---|
| author | Wen, Yaoxinog |
| author_facet | Wen, Yaoxinog |
| citation_txt | Difference Equation for Quintic 3-Fold. Yaoxinog Wen. SIGMA 18 (2022), 043, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type of -difference equations at = 0 and = ∞. We consider two special cases; the first is the -difference equation of the -theoretic -function of the quintic, which is degree 25; we use Adams' method to find the extra 20 solutions at = 0. The second special case is a Fuchsian case, which is confluent to the differential equation of the cohomological -function of the quintic. We compute the connection matrix and study the confluence of the -difference structure.
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| first_indexed | 2026-03-17T20:38:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211625 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T20:38:36Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wen, Yaoxinog 2026-01-07T13:40:24Z 2022 Difference Equation for Quintic 3-Fold. Yaoxinog Wen. SIGMA 18 (2022), 043, 25 pages 1815-0659 2020 Mathematics Subject Classification: 14N35; 33D90; 39A13 arXiv:2011.07527 https://nasplib.isofts.kiev.ua/handle/123456789/211625 https://doi.org/10.3842/SIGMA.2022.043 In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type of -difference equations at = 0 and = ∞. We consider two special cases; the first is the -difference equation of the -theoretic -function of the quintic, which is degree 25; we use Adams' method to find the extra 20 solutions at = 0. The second special case is a Fuchsian case, which is confluent to the differential equation of the cohomological -function of the quintic. We compute the connection matrix and study the confluence of the -difference structure. The author would like to thank Professor Yongbin Ruan for suggesting this problem and for valuable discussions. Thanks are also due to Professor Shuai Guo and Dr. Yizhen Zhao for their helpful discussion. This work was initiated during the author’s stay at the Institute for Advanced Study in Mathematics (IASM) at Zhejiang University. The author would like to express his thanks to IASM, Professor Bohan Fan, Professor Huijun Fan, and Peking University for their helpful support during this visit. The author wants to thank the anonymous referees who helped improve the paper a lot. The author is supported by a KIAS Individual Grant (MG083901) at the Korea Institute for Advanced Study. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Difference Equation for Quintic 3-Fold Article published earlier |
| spellingShingle | Difference Equation for Quintic 3-Fold Wen, Yaoxinog |
| title | Difference Equation for Quintic 3-Fold |
| title_full | Difference Equation for Quintic 3-Fold |
| title_fullStr | Difference Equation for Quintic 3-Fold |
| title_full_unstemmed | Difference Equation for Quintic 3-Fold |
| title_short | Difference Equation for Quintic 3-Fold |
| title_sort | difference equation for quintic 3-fold |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211625 |
| work_keys_str_mv | AT wenyaoxinog differenceequationforquintic3fold |