摘要翻译：
文献[12]中确定了有理椭圆曲线E上Heegner点的Neron-Tate高度满足所谓Heegner条件的二次判别式上的平均值的前序项。此外，还对二阶项进行了推测。本文证明了这个猜想的二阶项是正确的；这在剩余的任期内产生了省电。等差数列中GL(2)-尖点形式的Fourier系数的对消是证明的核心。
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英文标题：
《Comportement asymptotique des hauteurs des points de Heegner》
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作者：
Guillaume Ricotta, Nicolas Templier
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  The leading order term for the average, over quadratic discriminants satisfying the so-called Heegner condition, of the Neron-Tate height of Heegner points on a rational elliptic curve E has been determined in [12]. In addition, the second order term has been conjectured. In this paper, we prove that this conjectured second order term is the right one; this yields a power saving in the remainder term. Cancellations of Fourier coefficients of GL(2)-cusp forms in arithmetic progressions lie in the core of the proof.
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PDF链接：
https://arxiv.org/pdf/0807.2930