Use a proof by contradiction to prove general counting principl... | Filo
Use a proof by contradiction to prove general counting principl... …
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Visualizing Riemann's Explicit Formula #RiemannZeta #complexanalysis #numbertheory #PrimeNumbers
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Visualizing Riemann's Explicit Formula #RiemannZeta #complex…
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Part 4: I discuss the connection between the zeros of the Riemann zeta function and the distribution of prime numbers. The zeros control the oscillations of the prime counting function, $\\pi(x)$. The prime counting function is roughly approximated by $li(x)$, which is the logarithmic integral and is basically the number one would expect. The difference between $\\pi(x)$ and $li(x)$ contributes a term like $\\cos(t \\log x)$. We note that if Riemann Hypothesis is true, prime numbers are spread s
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