AI 中文总结
研究算术级数中最小素数与最小二次非剩余问题，结合广义黎曼假设中零点水平位置与对关联视角，在相关假设下建立更精确估计，为狄利克雷L函数对关联现象与经典问题提供新联系。
AI 中文摘要
广义黎曼假设（GRH）长期以来定义了算术级数中最小素数和最小二次非剩余的预期界限。然而，该假设主要关注非平凡零点的水平位置。本文表明，纳入这些零点的垂直间距（即对关联）能让我们超越这些经典界限。通过结合这两个零点分布视角，在GRH和特定对关联假设下为这两个问题建立了更精确估计，为狄利克雷L函数的对关联现象与这两个经典问题提供了新联系。
英文摘要
The Generalized Riemann Hypothesis (GRH) has long defined the expected bounds for the smallest prime in an arithmetic progression and the least quadratic non-residue. However, this hypothesis primarily addresses the horizontal location of non-trivial zeros. In this paper, we show that incorporating the vertical spacing--or pair-correlation--of these zeros allows us to surpass these classical bounds. By combining these two zero-distribution perspectives, we establish sharper estimates for both problems under GRH and specific pair-correlation hypotheses, thereby providing a new link between pair-correlation phenomena for Dirichlet L-functions and these two classical problems.
Comments26 pages
