Abstract: In addition to being a classical subject of research, information about roots of quadratic congruences such as x^2 - D = 0 mod m is a crucial input to many methods in number theory. Moreover, due to Gauss's parametrization by binary quadratic forms, powerful tools like the spectral theory of automorphic forms can be applied to study the statistical distribution of the roots. In joint work with Jens Marklof, we find a new geometric/dynamic realization of the roots that allows us to study the fine-scale distribution using techniques from homogeneous dynamics. In particular, we derive an explicit expression for their pair correlation density.
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Conference Number：858 6869 7828
Password：289820
