Theta series and number fields: theorems and experiments

 

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Detalles Bibliográficos
Autores: Barquero Sánchez, Adrián Alberto, Mantilla Soler, Guillermo, Ryan, Nathan C.
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:https://www.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
Access Level:acceso abierto
Palabra clave:Quartic fields
Theta series