Taiwanese Journal of Mathematics

Numerical Invariants of Totally Imaginary Quadratic $\mathbb{Z}[\sqrt{p}]$-orders

Jiangwei Xue, Tse-Chung Yang, and Chia-Fu Yu

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Let $A$ be a real quadratic order of discriminant $p$ or $4p$ with a prime $p$. In this paper we classify all proper totally imaginary quadratic $A$-orders $B$ with index $w(B) = [B^\times : A^\times] \gt 1$. We also calculate numerical invariants of these orders including the class number, the index $w(B)$ and the numbers of local optimal embeddings of these orders into quaternion orders. These numerical invariants are useful for computing the class numbers of totally definite quaternion algebras.

Article information

Taiwanese J. Math., Volume 20, Number 4 (2016), 723-741.

First available in Project Euclid: 1 July 2017

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Zentralblatt MATH identifier

Primary: 11R52: Quaternion and other division algebras: arithmetic, zeta functions 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]

class number formula arithmetic of quaternion algebras


Xue, Jiangwei; Yang, Tse-Chung; Yu, Chia-Fu. Numerical Invariants of Totally Imaginary Quadratic $\mathbb{Z}[\sqrt{p}]$-orders. Taiwanese J. Math. 20 (2016), no. 4, 723--741. doi:10.11650/tjm.20.2016.6464. https://projecteuclid.org/euclid.twjm/1498874487

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