Heegner点的等分布与三元二次型
Equidistribution of Heegner Points and Ternary Quadratic Forms
摘要：
证明了Heegner点的Galois轨道关于惰性素数约化映射的等分布结果。参数是基于两种不同的技术：整数的原始表示的二次型和Heegner点的分布关系。我们的结果推广了一个等分布定理建立的Cornut和Vatsal在这个意义上，我们允许的基本判别式和导体的增长。此外，对于固定的基本判别式和可变的导体，我们给出了一个有效的满射定理，证明了Heegner点到超奇异点的约化映射在固定的惰性素数上是满射的.我们的结果适用于Kolyvagin在构造Heegner点Euler系统时所考虑的情况。
英文摘要：
We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system.
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