# Tagged Questions

Questions on the famed $\zeta(s)$ function of Riemann, and its properties.

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### Why do you need to prove the error term goes to zero for the complete derivation of the Euler Product Formula?

I am doing a project on the Riemann-Zeta Function which begins by examining the Euler Product Formula. I understand the proof up until the point where it is made 'rigorous'. In other words, I ...
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### Argument of the Riemann zeta function on Re(s)=1

I refer to the lovely answer to this question. Is there an exact formula for the argument of the Riemann zeta function? Specifically, I would like to know the arguments along the line Re$(s)=1$. Some ...
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### what is the value of Chebyshev function at non-integer value?

What is the value of Chebyshev $\psi(x)$ function at non-integer values ? For example, what is the value of $\psi(3.56)$? I have seen, in same place, it seems that $$\psi(3.56)=\psi(3)$$ And in ...
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### I think I found a flaw in Riemann Zeta Function Regularization

I think I may have found a flaw in how Zeta Regularization works. As we all know, it's very famous for proving that $1+2+3+4+...=(-1/12).$ See here (5 rows of equations at the end of this post) •...
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### Does Riemann Hypothesis imply strong Goldbach Conjecture? [duplicate]

In Andrew Granville's 2007 paper: "REFINEMENTS OF GOLDBACH’S CONJECTURE, AND THE GENERALIZED RIEMANN HYPOTHESIS" He said: "an averaged strong form of Goldbach's conjecture is equivalent to the ...
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### Selberg's theorem, rotational invariance and circle on the Riemann sphere

If I'm not mistaken, Selberg proved that $\vert\zeta(1/2+it)\vert$ is normally distributed. But the normal distribution is known for its rotational invariance property and as a matter of fact, RH is ...
This is a detail from a proof in Ingham's Distribution of Prime Numbers, p. 91-92. He forms a Dirichlet integral and assumes for contradiction that the numerator $c(x)\geq 0.$ Then he bounds $f(s)$ in ...