Measures, modular forms, and summation formulas of Poisson type
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908603863007232 |
|---|---|
| author | Alfes, Claudia Kiefer, Paul Mazáč, Jan |
| author_facet | Alfes, Claudia Kiefer, Paul Mazáč, Jan |
| contents | In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour with respect to the metaplectic group. A familiar subset of such Fourier series comprises holomorphic modular forms. This allows us to construct $k$-spherical eigenmeasures and derive Poisson-type summation formulas, thereby recovering formulas of a similar nature established by Cohn-Gonçalves, Lev-Reti, and Meyer, among others. Additionally, we extend our results to higher dimensions, where Hilbert modular forms yield higher-dimensional $k$-spherical measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measures, modular forms, and summation formulas of Poisson type Alfes, Claudia Kiefer, Paul Mazáč, Jan Number Theory Mathematical Physics Classical Analysis and ODEs In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour with respect to the metaplectic group. A familiar subset of such Fourier series comprises holomorphic modular forms. This allows us to construct $k$-spherical eigenmeasures and derive Poisson-type summation formulas, thereby recovering formulas of a similar nature established by Cohn-Gonçalves, Lev-Reti, and Meyer, among others. Additionally, we extend our results to higher dimensions, where Hilbert modular forms yield higher-dimensional $k$-spherical measures. |
| title | Measures, modular forms, and summation formulas of Poisson type |
| topic | Number Theory Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2405.15620 |