论文标题
Chebyshev对椭圆曲线的偏见的新方面
A New Aspect of Chebyshev's Bias for Elliptic Curves over Function Fields
论文作者
论文摘要
这项工作考虑了功能字段上的非恒定椭圆曲线$ e $的质量数。我们证明，如果$ \ mathrm {rank}（e）> 0 $，那么Chebyshev存在偏见，否则Chebyshev存在偏向积极的偏见。主要的创新需要从深层黎曼假设对功能领域的假设进行的部分Euler产品的收敛。
This work considers the prime number races for non-constant elliptic curves $E$ over function fields. We prove that if $\mathrm{rank}(E) > 0$, then there exist Chebyshev biases towards being negative, and otherwise there exist Chebyshev biases towards being positive. The main innovation entails the convergence of the partial Euler product at the centre that follows from the Deep Riemann Hypothesis over function fields.
