Mean value problems of arithmetical functions play an important role in the study of analytic number theory, and they relate to many famous number theoretic problems.
算术函数的均值问题在解析数论研究中占有十分重要的位置，许多著名的数论难题都与之密切相关。
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The paper discusses what the arithmetical compliment of the power denoted by the exponent function (EP 'function) is and a new method of judging prime number with EP 'function.