On coefficients of Poincaré series and single-valued periods of modular forms
| العنوان: | On coefficients of Poincaré series and single-valued periods of modular forms |
|---|---|
| المؤلفون: | Tiago J. Fonseca |
| المصدر: | Research in the Mathematical Sciences |
| بيانات النشر: | Springer, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Pure mathematics, Modular form, Holomorphic function, Fourier coefficients, Field (mathematics), Harmonic (mathematics), 11F67, 32G20, 01 natural sciences, Poincaré series, Theoretical Computer Science, Mathematics (miscellaneous), 0103 physical sciences, 0101 mathematics, Fourier series, 11F30, 11F67, 32G20, 14J15, Mathematics, Modular motives, Mathematics - Number Theory, Applied Mathematics, Research, 010102 general mathematics, Single-valued periods, 16. Peace & justice, 11F30, Computational Mathematics, Weakly holomorphic modular forms, 010307 mathematical physics, 14J15, Series expansion |
| الوصف: | We prove that the field generated by the Fourier coefficients of weakly holomorphic Poincar\'e series of a given level $\Gamma_0(N)$ and weight $k\ge 2$ coincides with the field generated by the single-valued periods of a certain motive attached to $\Gamma_0(N)$. This clarifies the arithmetic nature of such Fourier coefficients and generalises previous formulas of Brown and Acres--Broadhurst giving explicit series expansions for the single-valued periods of some modular forms. Our proof is based on Bringmann--Ono's construction of harmonic lifts of Poincar\'e series. Comment: 36 pages. Final version |
| اللغة: | English |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::90ac78c1ff0d9e11f28a75153da9fae2Test https://ora.ox.ac.uk/objects/uuid:31e66b9b-55be-46c9-a450-78973084576cTest |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....90ac78c1ff0d9e11f28a75153da9fae2 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |