Fractional Parts of Bernoulli Numbers
نویسنده
چکیده
The sequence {B2}, {B4}, {B6}, ... is dense in the unit interval [0, 1], but it is not uniformly distributed [4]. Certain rational numbers appear with positive probability: 1/6 is most likely with probability 0.151..., 29/30 is next with probability 0.064... [5]. In fact, the limiting distribution F is piecewise linear with countably many jump discontinuities: F increases only when jumping (see Figure 1). We wonder, in particular, about the moments of F . By the von Staudt-Clausen theorem, the mean fractional part is [6]
منابع مشابه
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تاریخ انتشار 2007