解析数论非常幸运还有一个最为有名的未解决的问题，即黎曼假设。
Analytic number theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.
利用解析方法研究了平方剩余数的若干性质，并给出了平方剩余数对于两个常用数论函数的几个均值公式。
By using the analytic method some properties of the square residues are studied, and several (interesting) mean value formulas are given.
在结束这次讲话时，我愿通过再次说明，数论将在无论有还是没有黎曼假设的情况下继续繁荣，来强调我对于解析数论的拥护。
In concluding this talk I wish to emphasize my advocacy for analytic number theory by saying again that the theory flourishes with or without the Riemann hypothesis.
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。
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.
摘要最大模原理在复变函数论中占有重要的地位，是研究解析函数的有力工具。
Maximum modulus principle plays an important role in the complex analytics, and it is a powerful tool in studying the analytic function.
解析函数是复变函数论主要的研究对象，而解析函数的五个等价条件又贯穿了我们对复变函数论学习的全过程。
Analytic functions of complex variable function is the main object of study, and the five equivalent conditions of analytic functions penetrate the whole process of learning of complex function.
利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。
We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.
利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。
We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.
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