Littlewood问题的进一步研究

A further study on the problem of Littlewood

根据成礼智等在《数学的实践与认识》1998年第4期所提供的方法,将其定理1成立的区间由0≤r≤1扩充到0≤r≤2,定理2的常数因子由21/3改进到(1.9717)3/10,还得到了该序列在不减条件下的最佳常数.

According to the method provided by Cheng Li-zhi, et al in 《Mathematics in practice and theory》 Vol. 28 No. 4, the author extends the valid inteval of its Theorem 1 from 0≤r≤1 to 0≤r≤2 ,and improves the constant factor of Theorem 2 from 2^1/3 to （1. 9717）^3/10, as well as gets the optimum constant when this sequence is nondecreasing.