函数域的ζ零点随亏格趋于无穷时的启发式等分布
Zeta zeros of function fields heuristically equidistribute as genus goes to infinity
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中文总结 AI 辅助
该研究针对有限域上曲线平均类数增长率提出启发式方法，基于通用雅可比稳定上同调假设，证明曲线ζ函数零点随亏格趋于无穷时在圆上等分布。
中文摘要 AI 辅助
我们针对有限域$\boldsymbol{\frak{M}}_g(\boldsymbol{\frak{F}}_q)$中曲线的平均类数增长率提出一种启发式方法。该启发式基于通用雅可比的稳定上同调主导迹公式点计数的假设，遵循Achter等人的方法，证明其意味着此类曲线的ζ函数零点随亏格$g\to\boldsymbol{\frak{M}}_g(\boldsymbol{\frak{F}}_q)$趋于无穷时在圆上等分布。
英文摘要
We propose a heuristic for the growth rate of the average class number of curves in $\mathcal M_g(\mathbb F_q)$ as $g \to \infty$. We show that this heuristic implies that the zeros of the zeta functions of such curves become equidistributed on the circle as $g\to\infty$. Our heuristic is based on the assumption that the stable cohomology of the universal Jacobian dominates a point count using the trace formula, following the method of Achter et al.
