Prime numbers and the Riemann hypothesis

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1. ykonstantDec 2022
   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.
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2. abhghJul 2020
   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

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3. jesuslopJul 2026
   Apropos, Wikipedia says at a picture: "(Left) The von Mangoldt function, approximated by zeta zero waves.(Right) The Fourier transform of the von Mangoldt function gives a spectrum with imaginary parts of Riemann zeta zeros as spikes." [1]. [2] explains the details very gently, one can skip parts. So 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

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