Analytic Study for Pisot and Salem numbers

我们成功地改进了早期关于e^n的分数部分的下界的结果，其中e是自然对数的底，并且已知是超越的。这项研究是通过Pisot数和Salem数来完成的。关于Mahler测度问题(Lehmer问题)，我们可以把它归结为一个非线性泛函的极值问题。

We successfully improved the earlier results on the lower bounds for the fractional part of e^n, where e is the base of natural logarithm and is known to be transcendental. This study was accomplished through that of Pisot and Salem numbers. Concerning the problem on Mahler measures (Lehmer problem) we can reduce it to an extremal problem of some non-linear functional.