Regularity properties of $k$-Brjuno and Wilton functions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910371949838336 |
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| author | Lee, Seul Bee Marmi, Stefano Petrykiewicz, Izabela Schindler, Tanja I. |
| author_facet | Lee, Seul Bee Marmi, Stefano Petrykiewicz, Izabela Schindler, Tanja I. |
| contents | We study functions related to the classical Brjuno function, namely $k$-Brjuno functions and the Wilton function. Both appear in the study of boundary regularity properties of (quasi) modular forms and their integrals. We consider various possible versions of them, based on the $α$-continued fraction developments. We study their BMO regularity properties and their behaviour near rational numbers of their finite truncations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_07298 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Regularity properties of $k$-Brjuno and Wilton functions Lee, Seul Bee Marmi, Stefano Petrykiewicz, Izabela Schindler, Tanja I. Dynamical Systems Number Theory 30B70, 37F50, 32A50, 46F15, 32A37, 11F03 We study functions related to the classical Brjuno function, namely $k$-Brjuno functions and the Wilton function. Both appear in the study of boundary regularity properties of (quasi) modular forms and their integrals. We consider various possible versions of them, based on the $α$-continued fraction developments. We study their BMO regularity properties and their behaviour near rational numbers of their finite truncations. |
| title | Regularity properties of $k$-Brjuno and Wilton functions |
| topic | Dynamical Systems Number Theory 30B70, 37F50, 32A50, 46F15, 32A37, 11F03 |
| url | https://arxiv.org/abs/2106.07298 |