论文标题
GRH下的混合猜想
The mixing conjecture under GRH
论文作者
论文摘要
我们证明了Michel-venkatesh的混合猜想，用于在较大的判别物上进行集体群体在紧凑型算术表面上的较大判别点，该表面附着于有理Quaternion代数中的最大秩序。该证明是基于广义的Riemann假设的条件，而当分区代数不确定时，我们还假定Ramanujan的猜想。我们的方法提供了有效的速率，它基于自动形式的光谱理论及其$ l $ functions以及经典分析数理论的技术。
We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in rational quaternion algebras. The proof is conditional on the Generalized Riemann Hypothesis, and when the division algebra is indefinite we furthermore assume the Ramanujan conjecture. Our methods, which provide an effective rate, are based on the spectral theory of automorphic forms and their $L$-functions, as well as techniques in classical analytic number theory.
