Afshar Ardavan
Department of Mathematics, University College London, 25 Gordon Street, London, England.
Ramanujan J. 2021;56(2):729-742. doi: 10.1007/s11139-020-00299-2. Epub 2020 Aug 3.
We investigate the analogues, in , 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.
我们研究了拉马努金所研究的高度合成数在多项式情形下的类似物以及除数函数的最大阶。特别地，我们确定了一族不太稀疏的高度合成多项式，并利用它来计算除数函数在每个次数下最大值的对数，误差为一个常数，即使假设黎曼假设成立，该误差也比整数情形下的显著更小。
