- How was the importance of the zeta function discovered ?
- why do zeta function contain so much information ?
- What other areas of mathematics does it relate to ?
- Are there any books on the RH ?
- I've heard something about a connection with quantum physics – what's that about?
- Isn't there a connection with cryptography? Would a proof compromise the security of Internet communications and financial transactions?
- What are the Extended Riemann Hypothesis, Generalised RH?
Anton Vrdoljak
https://www.researchgate.net/post/Way_Riemann_Zeta_Function_is_Important
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Issam Kaddoura
Dear Aziz Elghazouani
It gains its importance due to the strong relationship between the Riemann Zetta function and prime numbers distribution.
Also, it is one of the Millenium open problems.
The Riemann Hypothesis is
The nontrivial zeros of ζ(s) have a real part equal to 1/2.
See the attached file.
Best regards
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Norbert Tihanyi
The Riemann Zeta function is very deeply connected to the distribution of the prime numbers. The error term in the prime number theorem is closely related to the position of the zeros of the Riemann Zeta function.
If the Riemann Hypothesis is true then the distribution of the prime numbers is definitely not random.
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