Meromorphic Continuation Of Global Zeta Function For Number Fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914771968720896 |
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| author | De, Subham |
| author_facet | De, Subham |
| contents | In the paper, we shall establish the existence of a meromorphic continuation of the Global Zeta Function $ζ(f,χ)$ of a Global Number Field $K$ and also deduce the functional equation for the same, using different properties of the idèle class group $\mathcal{C}_K^1$ of a global field $K$ extensively defined using basic notions of Adèles ($\mathbb{A}_{K}$) and Idèles ($\mathbb{I}_{K}$) of $K$, and also evaluating Fourier Transforms of functions $f$ on the space $\mathcal{S}(\mathbb{A}_{K})$ of Adèlic Schwartz-Bruhat Functions. A brief overview of most of the concepts required to prove our desired result have been provided to the readers in the earlier sections of the text. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12007 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Meromorphic Continuation Of Global Zeta Function For Number Fields De, Subham History and Overview Primary 11-02, 11R04, 11R37, 11M06, 11F70 . Secondary 11M41, 28C10, 11R56 In the paper, we shall establish the existence of a meromorphic continuation of the Global Zeta Function $ζ(f,χ)$ of a Global Number Field $K$ and also deduce the functional equation for the same, using different properties of the idèle class group $\mathcal{C}_K^1$ of a global field $K$ extensively defined using basic notions of Adèles ($\mathbb{A}_{K}$) and Idèles ($\mathbb{I}_{K}$) of $K$, and also evaluating Fourier Transforms of functions $f$ on the space $\mathcal{S}(\mathbb{A}_{K})$ of Adèlic Schwartz-Bruhat Functions. A brief overview of most of the concepts required to prove our desired result have been provided to the readers in the earlier sections of the text. |
| title | Meromorphic Continuation Of Global Zeta Function For Number Fields |
| topic | History and Overview Primary 11-02, 11R04, 11R37, 11M06, 11F70 . Secondary 11M41, 28C10, 11R56 |
| url | https://arxiv.org/abs/2307.12007 |