New formulas for zeta constants are obtained based on a number theoretic approach that is used in proving irrationality of some classical constants. Using these formulas, one can approximate zeta constants and their combinations by rational fractions and construct a new efficient evaluation method for them.

中文翻译：

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基于数论方法的Zeta常数评价方法

zeta 常数的新公式是基于用于证明一些经典常数的无理性的数论方法获得的。使用这些公式，人们可以通过有理分数近似 zeta 常数及其组合，并为它们构建一种新的有效评估方法。