我最近把《数论图解》（Illustrated Theory of Numbers）作为礼物送给了一位朋友，它的插图确实极美。就其插图和讲解水平而言，我还推荐《素数与黎曼猜想》（Prime Numbers and the Riemann Hypothesis）[1]。[1] https://www.amazon.com/gp/product/1107499437
I recently gifted Illustrated Theory of Numbers to a friend, and it is indeed beautifully illustrated. I would also recommend "Prime Numbers and the Riemann Hypothesis" for its illustrations and exposition [1]. [1] https://www.amazon.com/gp/product/1107499437
非常棒的帖子！如果要寻找一本关于素数定理（以及黎曼猜想）的绝佳入门读物，我推荐巴里·梅祖尔（Barry Mazur）和威廉·斯坦因（William Stein）合著的《素数与黎曼猜想》（Prime Numbers and the Riemann Hypothesis）。全书由篇幅很短的章节构成，每一章阐明一个核心观点，我觉得这种编排太棒了。
Very good post! For an excellent introduction to the prime number theorem (and the Riemann Hypothesis), I recommend Prime Numbers and the Riemann Hypothesis, by Barry Mazur and William Stein. It is structured in small chapters, each illuminating one idea, and I find this fantastic.
…this is a machine with input a function very close to prime counts, and outputs info about zeta zeros. And the machine is Fourier transform. [1] https://en.wikipedia.org/wiki/Von_Mangoldt_function [2] Prime numbers and the Riemann hypothesis. Mazur, Stein
我最近把《数论图解》（Illustrated Theory of Numbers）作为礼物送给了一位朋友，它的插图确实极美。就其插图和讲解水平而言，我还推荐《素数与黎曼猜想》（Prime Numbers and the Riemann Hypothesis）[1]。[1] https://www.amazon.com/gp/product/1107499437
I recently gifted Illustrated Theory of Numbers to a friend, and it is indeed beautifully illustrated. I would also recommend "Prime Numbers and the Riemann Hypothesis" for its illustrations and exposition [1]. [1] https://www.amazon.com/gp/product/1107499437
非常棒的帖子！如果要寻找一本关于素数定理（以及黎曼猜想）的绝佳入门读物，我推荐巴里·梅祖尔（Barry Mazur）和威廉·斯坦因（William Stein）合著的《素数与黎曼猜想》（Prime Numbers and the Riemann Hypothesis）。全书由篇幅很短的章节构成，每一章阐明一个核心观点，我觉得这种编排太棒了。
Very good post! For an excellent introduction to the prime number theorem (and the Riemann Hypothesis), I recommend Prime Numbers and the Riemann Hypothesis, by Barry Mazur and William Stein. It is structured in small chapters, each illuminating one idea, and I find this fantastic.
……这是一台输入极其接近素数计数的函数、输出关于 zeta 零点信息的机器。而这台机器就是傅里叶变换。[1] https://en.wikipedia.org/wiki/Von_Mangoldt_function [2]《素数与黎曼猜想》，梅祖尔、斯坦因
…this is a machine with input a function very close to prime counts, and outputs info about zeta zeros. And the machine is Fourier transform. [1] https://en.wikipedia.org/wiki/Von_Mangoldt_function [2] Prime numbers and the Riemann hypothesis. Mazur, Stein