Spectrum of p-adic linear differential equations I: The shape of the spectrum
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| Format: | Preprint |
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2021
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| _version_ | 1866916090132561920 |
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| author | Azzouz, Tinhinane A. |
| author_facet | Azzouz, Tinhinane A. |
| contents | This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with constant coefficients or over a field of formal power series. In this paper, we investigate the spectrum of $p$-adic differential equations at a generic point on a quasi-smooth curve. This analysis allows us to establish a significant connection between the spectrum and the spectral radii of convergence of a differential equation when considering the affine line. Furthermore, the spectrum offers a more detailed decomposition compared to Robba's decomposition based on spectral radii. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_03548 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Spectrum of p-adic linear differential equations I: The shape of the spectrum Azzouz, Tinhinane A. Number Theory Spectral Theory Primary 12H25, Secondary 14G22, 11F72 This paper extends our previous works arXiv:1802.07306 [math.NT], arXiv:1808.02382 [math.NT] on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with constant coefficients or over a field of formal power series. In this paper, we investigate the spectrum of $p$-adic differential equations at a generic point on a quasi-smooth curve. This analysis allows us to establish a significant connection between the spectrum and the spectral radii of convergence of a differential equation when considering the affine line. Furthermore, the spectrum offers a more detailed decomposition compared to Robba's decomposition based on spectral radii. |
| title | Spectrum of p-adic linear differential equations I: The shape of the spectrum |
| topic | Number Theory Spectral Theory Primary 12H25, Secondary 14G22, 11F72 |
| url | https://arxiv.org/abs/2111.03548 |