It is well known that Riemann zeta function describe the prime distribution using many indirect methods like prime counting function and prime number theorem also von mangoldt function and also prime counting function such that there is a clear mathematical formula for computing probability to get a prime number and there is a huge topic talk about Randomness in prime and do not forgot Random matrix , now what i know if any function discribe distribution of such random variable this means that is a probability density function , Now my question here why we do not saw any formula show that Riemann zeta function is a density function such that $\int_{0}^{\infty} \zeta(s)=1$ ?
2026-03-29 19:16:32.1774811792
Why Riemann zeta function is not a density function however it describe prime distribution?
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