Lecture----数学院晨兴数学中心

Title:	Counting zeros in quaternion algebras using Jacobi forms
Speaker:	Prof. Haigang Zhou (Tongji University)
Time:	2016-10-20, 15:15-16:15
Place:	610
Abstract:	We use the theory of Jacobi forms to study the number of elements in a maximal order of a definite quaternion algebra over the field of rational numbers whose characteristic polynomial equals a given polynomial. A certain weighted average of such numbers equals (up to some trivial factors) the Hurwitz class number $H(4n-r^2)$. As a consequence we obtain new proofs for Eichler's trace formula and for formulas for the class and type number of definite quaternion algebras. As a secondary result we derive explicit formulas for Jacobi Eisenstein series of weight~$2$ on $\Gamma_0(N)$ and for the action of Hecke operators on Jacobi theta series associated to maximal orders of definite quaternion algebras.
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