AI 中文总结
该研究针对S. J. Miller的负偏差猜想，确定勒让德椭圆曲线族高阶矩的偏差，证明低阶项平均为零或负，计算了第三、第四矩，所得赫维茨类数相关结果或具其他应用价值。
AI 中文摘要
针对S. J. Miller的负偏差猜想，我们确定了勒让德椭圆曲线族高阶矩的偏差。我们证明，对于偶数矩和奇数矩，每个低阶项平均要么为零要么为负，并明确计算了第三和第四矩。过程中证明的算术级数中赫维茨类数的结果可能对其他应用有用。
英文摘要
We determine the bias in higher moments of the Legendre family of elliptic curves in view of the Negative Bias Conjecture of S. J. Miller. We show that every lower order term is either zero or negative on average for both even and odd moments, and explicitly compute the third and fourth moment. The results about Hurwitz class numbers in arithmetic progressions which we prove in the process may be useful for other applications.
Comments36 pages, comments are welcome! Additional details contained in the source file
