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Title:
Lecture #1: Tools for counting quaternion algebras
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Abstract:
In this lecture, we will introduce some classical techniques from analytic number theory and show how they can be used to count quaternion algebras over number elds subject to various constraints. Because of the correspondence between maximal subelds of quaternion algebras and geodesics on arithmetic hyperbolic manifolds, these counts can be used to produce quantitative results in spectral geometry.
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