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Abstract We study the embedding problem for commutative orders into Eichler orders in definite quaternion algebras over the rationals by using methods from the theory of quadratic forms, specifically, Minkowski–Siegel's… Click to show full abstract
Abstract We study the embedding problem for commutative orders into Eichler orders in definite quaternion algebras over the rationals by using methods from the theory of quadratic forms, specifically, Minkowski–Siegel's formula for the representation mass. We characterize when the Gaussian or Eisenstein integers embed into some but not all classes in the genus of an Eichler order. We also give an application to the theory of supersingular elliptic curves.
Keywords:
quaternion algebras;
selectivity definite;
definite quaternion
Journal Title: Journal of Number Theory
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Number Theory
Year Published: 2018
Link to full text (if available)
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recommendations!