Computing quadratic modular symbols

Details Computing quadratic modular symbols Computing quadratic modular symbols

2012-04-25

arxiv.org/abs/1204.5670v1

Mathematics

Number Theory

12 pages and 2 figures. Comments are welcome

Scientific paper

Bayer and Blanco-Chac\'on have recently defined the quadratic modular symbol for the Shimura curve $X(D,N)$ attached to the Eichler order $\mathcal{O}(D,N)$ of an indefinite quaternion $\mathbb{Q}$-algebra of discriminant $D$. In this paper we give an algorithm which, for a finite family of these Shimura curves, decomposes closed homology classes into linear combinations of distinguished classes. We also give a cohomological interpretation of the quadratic modular symbol.

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