论文标题
高度复合的多项式和除法函数的最大顺序在$ \ mathbb {f} _q [t] $中
Highly Composite Polynomials and the maximum order of the Divisor Function in $\mathbb{F}_q[t]$
论文作者
论文摘要
我们在$ \ mathbb {f} _q [t] $中调查了类似物的高度复合数字和除数函数的最大顺序，如Ramanujan所研究。特别是，我们确定了一个高度复合多项式的家族，该家族并不太稀疏，我们使用它来计算每个程度上除法的最大值的对数，直到一个常数的误差，即使在整数中，它也比整数的误差要小得多，甚至假设假设Riemann假设。
We investigate the analogues, in $\mathbb{F}_q[t]$, of highly composite numbers and the maximum order of the divisor function, as studied by Ramanujan. In particular, we determine a family of highly composite polynomials which is not too sparse, and we use it to compute the logarithm of the maximum of the divisor function at every degree up to an error of a constant, which is significantly smaller than in the case of the integers, even assuming the Riemann Hypothesis.
