The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation
Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equations and integration problems are reg...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214180 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation. Veronica Fantini and Aaron Fenyes. SIGMA 21 (2025), 101, 69 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862719067105787904 |
|---|---|
| author | Fantini, Veronica Fenyes, Aaron |
| author_facet | Fantini, Veronica Fenyes, Aaron |
| citation_txt | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation. Veronica Fantini and Aaron Fenyes. SIGMA 21 (2025), 101, 69 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equations and integration problems are regular in this sense. By taking a geometric perspective on the Laplace and Borel transforms, we also clarify why ''Borel regular'' solutions are associated with special points on the Borel plane. The particular classes of problems we look at are level 1 ODEs and exponential period integrals over one-dimensional Lefschetz thimbles. To expand the variety of examples available in the literature, we treat various examples of these problems in detail.
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| first_indexed | 2026-03-20T21:57:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214180 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T21:57:23Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fantini, Veronica Fenyes, Aaron 2026-02-20T07:53:09Z 2025 The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation. Veronica Fantini and Aaron Fenyes. SIGMA 21 (2025), 101, 69 pages 1815-0659 2020 Mathematics Subject Classification: 34M25; 34M30; 34M40; 40G10; 41A60 arXiv:2407.01412 https://nasplib.isofts.kiev.ua/handle/123456789/214180 https://doi.org/10.3842/SIGMA.2025.101 Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equations and integration problems are regular in this sense. By taking a geometric perspective on the Laplace and Borel transforms, we also clarify why ''Borel regular'' solutions are associated with special points on the Borel plane. The particular classes of problems we look at are level 1 ODEs and exponential period integrals over one-dimensional Lefschetz thimbles. To expand the variety of examples available in the literature, we treat various examples of these problems in detail. This paper is a result of the ERC-SyG project, Recursive and Exact New Quantum Theory (ReNewQuantum), which received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 810573. We thank Fondation Mathématique Jacques Hadamard for supporting the visit of the second author at IHÉS, under the program Junior Scientific Visibility. We thank Frédéric Fauvet, Maxim Kontsevich, Andrew Neitzke, and David Sauzin for fruitful discussions and suggestions. We thank the referees for their careful reading, thoughtful comments, and useful references. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation Article published earlier |
| spellingShingle | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation Fantini, Veronica Fenyes, Aaron |
| title | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation |
| title_full | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation |
| title_fullStr | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation |
| title_full_unstemmed | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation |
| title_short | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation |
| title_sort | regularity of odes and thimble integrals with respect to borel summation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214180 |
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