What does the Riemann zeta function have to do with the distribution of primes?
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What does the Riemann zeta function have to do with the distribution of primes?
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Re: What does the Riemann zeta function have to do with the distribution of primes?
#2What is the relationship between Riemann zeta function and Zipf's law? And between words and primes?
Re: What does the Riemann zeta function have to do with the distribution of primes?
#3Personally I’ve found this article a much more approachable overview to the question in the title: https://golem.ph.utexas.edu/category/2019/09/the_riemann_hyp...
Re: What does the Riemann zeta function have to do with the distribution of primes?
#4And as if all of that were not head-exploding enough, I'm still searching for an implementation of the zeta function for complex arguments...
Re: What does the Riemann zeta function have to do with the distribution of primes?
#5Stupid question on toilet: if prime numbers are 1s and other integers are 0s. What do we get from this “digital” landscape?
Re: What does the Riemann zeta function have to do with the distribution of primes?
#6Stupid question on toilet: if prime numbers are 1s and other integers are 0s. What do we get from this “digital” landscape?
The first-order difference of the prime-counting function: https://en.wikipedia.org/wiki/Prime-counting_function
Re: What does the Riemann zeta function have to do with the distribution of primes?
#7Stupid question on toilet: if prime numbers are 1s and other integers are 0s. What do we get from this “digital” landscape?
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Re: What does the Riemann zeta function have to do with the distribution of primes?
#8Although the author turned out to be a fairly despicable person, Prime Obsession is an absolutely wonderful book on this subject.
Re: What does the Riemann zeta function have to do with the distribution of primes?
#9I love that this is a site solely dedicated to the subject of interesting Diophantine equations, written by two mathematics PhD students. Going deep on a narrow focus, I respect that approach.
The article itself feels a bit long without a satisfying payoff at end. But then again, the journey is entertaining even for a non-specialist, and the lack of a strong conclusion is due to the unsolved problem of the Riemann hypothesis. The open-ended question is probably irresistible for some personality types that can't stand the suspense and demand a resolution.
Perhaps a way to strengthen the ending is to explain why the question of the distribution of prime numbers is worth solving, and what are the larger implications.
Re: What does the Riemann zeta function have to do with the distribution of primes?
#10Stupid question on toilet: if prime numbers are 1s and other integers are 0s. What do we get from this “digital” landscape?
If you plot the positive integers two-dimensionally in a square spiral arrangement, eg.
5 4 3
6 1 2
7 8 9