论文标题
Vinogradov问题的模块化类似物
A modular analogue of a problem of Vinogradov
论文作者
论文摘要
给定一个原始的，非CM的，全型尖缘形式$ f $，带有归一化的傅立叶系数$ a（n）$，并给定间隔$ i \ subset [-2，2] $，我们研究了最小的prime $ p $，使得$ a（p）\ in I $ $ $。这可以看作是vinogradov问题上最小二次的非遗留物的模块化形式类似物。我们在$ p $上获得了强大的明确界限，具体取决于$ f $的分析导体的某些特定选择$ i $。
Given a primitive, non-CM, holomorphic cusp form $f$ with normalized Fourier coefficients $a(n)$ and given an interval $I\subset [-2, 2]$, we study the least prime $p$ such that $a(p)\in I$ . This can be viewed as a modular form analogue of Vinogradov's problem on the least quadratic non-residue. We obtain strong explicit bounds on $p$, depending on the analytic conductor of $f$ for some specific choices of $I$.
