论文标题
功能字段短暂残留类别中的素数差异
Variance of primes in short residue classes for function fields
论文作者
论文摘要
Keating和Rudnick在算术过程中衍生出差异公式，用于算术阶段和函数场设置中的短间隔。在这里，我们考虑了计算算术进展和短间隔中素数方差的混合问题。基廷和鲁德尼克（Rudnick）使用一项涉及将短时间间隔转化为算术进程。我们遵循他们的方法，但除了将这种涉及到算术进程外。当模量$ q $是$ \ mathbb {f} _q [t] $中的多项式时，这会创建双重算术进度，以便$ q（0）\ not = 0 $。后者是我们在整个论文中保持的限制。最后，我们讨论了放松这种情况所需的内容。
Keating and Rudnick derived asymptotic formulas for the variances of primes in arithmetic progressions and short intervals in the function field setting. Here we consider the hybrid problem of calculating the variance of primes in intersections of arithmetic progressions and short intervals. Keating and Rudnick used an involution to translate short intervals into arithmetic progressions. We follow their approach but apply this involution, in addition, to the arithmetic progressions. This creates dual arithmetic progressions in the case when the modulus $Q$ is a polynomial in $\mathbb{F}_q[T]$ such that $Q(0)\not=0$. The latter is a restriction which we keep throughout our paper. At the end, we discuss what is needed to relax this condition.
