Analytic number theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.

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。

youdao

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.

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。

youdao

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。

youdao

But for most encryption systems, especially the Public Key systems that are widely used by the banks, you need to know very sophisticated number theory, analytic number theory, elliptical theory.

NPR: The Math Behind Pellicano's Code