Theta series and number fields: theorems and experiments
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| Autores: | , , |
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| Formato: | artículo original |
| Fecha de Publicación: | 2021 |
| Descripción: | Let d and n be positive integers and let K be a totally real number field of discriminant d and degree n. We construct a theta series $\theta_K \in \mathcal{M}_{d, n}$ where $\mathcal{M}_{d, n}$ is a space of modular forms defined in terms of n and d. Moreover, if d is square free and n is at most 4 then $\theta_K$ is a complete invariant for K. We also investigate whether or not the collection of $\theta$-series, associated to the set of isomorphism classes of quartic number fields of a fixed squarefree discriminant d, is a linearly independent subset of $\mathcal{M}_{d, 4}$. This is known to be true if the degree of the number field is less than or equal to 3. We give computational and heuristic evidence suggesting that in degree 4 these theta series should be independent as well. |
| País: | Kérwá |
| Institución: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/84376 |
| Acceso en línea: | https://link.springer.com/article/10.1007/s11139-021-00394-y#article-info https://hdl.handle.net/10669/84376 https://doi.org/10.1007/s11139-021-00394-y |
| Palabra clave: | Quartic fields Theta series |