Counting quaternion algebras, with applications to spectral geometry

Abstract: We will introduce some classical techniques from analytic number theory and show how they can be used to count quaternion algebras over number fields subject to various constraints. Because of the correspondence between maximal subfields of quaternion algebras and geodesics on arithmetic hyperbolic manifolds, these counts can be used to produce quantitative results in spectral geometry. This talk is based on joint work with B. Linowitz, D. B. McReynolds, and P. Pollack.

number theory

Audience: researchers in the topic

EIMI Number Theory Seminar

Series comments: Password: the number of quadratic nonresidues modulo 23