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Optimal spinor selectivity for quaternion orders.
- Source :
-
Journal of Number Theory . Feb2024, Vol. 255, p166-187. 22p. - Publication Year :
- 2024
-
Abstract
- Let D be a quaternion algebra over a number field F , and G be an arbitrary genus of O F -orders of full rank in D. Let K be a quadratic field extension of F that embeds into D , and B be an O F -order in K that can be optimally embedded into some member of G. We provide a necessary and sufficient condition for B to be optimally spinor selective for the genus G , which generalizes previous existing optimal selectivity criterions for Eichler orders as given by Arenas, Arenas-Carmona and Contreras, and by Voight independently. This allows us to obtain a refinement of the classical trace formula for optimal embeddings, which will be called the spinor trace formula. When G is a genus of Eichler orders, we extend Maclachlan's relative conductor formula for optimal selectivity from Eichler orders of square-free levels to all Eichler orders. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 255
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 173456985
- Full Text :
- https://doi.org/10.1016/j.jnt.2023.08.001