论文标题
甚至Zeta常数的非理性指数
Irrationality Exponents For Even Zeta Constants
论文作者
论文摘要
令$ k \ geq 1 $为一个小的固定整数。有理近似值$ \ weled | p/q-π^{k} \ right |> 1/q^{μ（π^k）} $的不合理数量$π^{k} $远离零。非理性指数$μ（π^k）$的一般结果将在这里证明。偶数参数的非理性指数$ 2K $与均匀的Zeta常数$ζ（2k）$相对应。还提供并解释了几种情况的特定结果和数值数据$ k = 2 $和$ k = 3 $。
Let $k\geq 1$ be a small fixed integer. The rational approximations $\left |p/q-π^{k} \right |>1/q^{μ(π^k)}$ of the irrational number $π^{k}$ are bounded away from zero. A general result for the irrationality exponent $μ(π^k)$ will be proved here. The irrationality exponents for the even parameters $2k$ correspond to those for the even zeta constants $ζ(2k)$. The specific results and numerical data for a few cases $k=2$ and $k=3$ are also presented and explained.
