dc.creator | Barquero Sánchez, Adrián Alberto | |
dc.creator | Mantilla Soler, Guillermo | |
dc.creator | Ryan, Nathan C. | |
dc.date.accessioned | 2021-09-02T14:11:35Z | |
dc.date.available | 2021-09-02T14:11:35Z | |
dc.date.issued | 2021-03-01 | |
dc.identifier.citation | https://link.springer.com/article/10.1007/s11139-021-00394-y#article-info | |
dc.identifier.uri | https://hdl.handle.net/10669/84376 | |
dc.description.abstract | 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. | es_ES |
dc.language.iso | eng | es_ES |
dc.source | The Ramanujan Journal, pp.1-12 | es_ES |
dc.subject | Quartic fields | es_ES |
dc.subject | Theta series | es_ES |
dc.title | Theta series and number fields: theorems and experiments | es_ES |
dc.type | artículo original | |
dc.identifier.doi | https://doi.org/10.1007/s11139-021-00394-y | |
dc.description.procedence | UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemática | es_ES |
dc.description.procedence | UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA) | es_ES |
dc.identifier.codproyecto | 821-B8-285 | |