# Questions tagged [riemann-hypothesis]

Questions on the Riemann hypothesis, a conjecture on the behavior of the complex zeros of the Riemann $\zeta$ function. You might want to add the tag [riemann-zeta] to your question as well.

292 questions
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### Proof by contradiction and ZF set theory

The following is quoted from Sir Michael Atiyah's draft proof of Riemann Hypothesis, Section 5, stating that 'To be explicit, the proof of RH in this paper is by contradiction and this is not accepted ...
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### Theorem 14.25(A) in Titchmarsh “The theory of the Riemann zeta-function”

In Titchmarsh's book "The theory of the Riemann zeta-function" there's theorem 14.25(A) on page 369 of the second edition where a summand $1/\zeta(s)$ appears out of the blue, so it seems... Oh, I do ...
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### What is the mass center of the Riemann Zeta Function across the critical line?

I just came with the idea: what is the center of mass of the Riemann Zeta Function across the critical line? I mean: when you plot the parametric graph across the critical line, you get the famous ...
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### Is there an analytic function with zeroes only at $-2n$, and zeroes at $\frac12\pm it$, and further, symmetric zeroes within the critical strip?

Is there an analytic function with zeroes only at: every $-2n$, $\frac12\pm it$, and at least one at $\frac12\pm\epsilon\pm it$ where $0<\epsilon<\frac12, t\neq0$ (and these zeroes observing ...
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### Unclear multiplication with Riemann zeta functional equation with eta

In the region 0 < Re(s) < 1 we know that $$\zeta(s) = 1/(1-2^{1-s}) \sum_1^\infty (-1)^{n+1}/n^s\,.$$ This is a multiplication of two complex numbers. Question 1: Am I right to suppose ...
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### Clarrification Regarding the Robin Inequality

I just read a paper related to the Robin Inequality, and the abstract read: "Abstract. Let σ(n) denote the sum of divisors function. In this paper we give a simple proof of the Robin inequality (R): ...
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### Questions and concerns

I would like to know if solving the riemann hypothesis as well as the twin prime conjecture are still questions within mathematics? I have been unable to find credible resources.
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### Riemann-Zeta Zeros and Quasicrystals

I came across quasicrystals in the Wikipedia page for the Riemann Hypothesis and then followed the references. On page 215 of Birds and Frogs Dyson makes the claim If the Riemann hypothesis is true,...
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### How is the Riemann zeta function $\zeta(s)$ determined by its values in a small open disc?

This question pertains to the following quote from chapter 7 section 9 of "Summing it Up: From One Plus One to Modern Number Theory" by Avner Ash and Robert Gross: "What makes the Riemann ...
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### Zeros of Riemann Zeta Function- Euler Product and Functional Equation

The problem statement, all variables and given/known data Question Use the functional equation to show that for : a) $k \in Z^+$ that $\zeta (-2k)=0$ b) Use the functional equation and the euler ...
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### Riemann hypothesis, random walks and Möbius function

How to show that the Riemann hypothesis, random walks and the Möbius function are related or even equivalent? I was reading the paper Randomness and Pseudorandomness by Avi Wigderson, but to me the ...