# Tagged Questions

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.

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### Wouldn't the asymptotes of the 2D projection of the inverse of the Riemann Zeta function show the real part of all the non-trivial zeros?

Can somebody provide a visualization of $z=\frac{1}{\zeta(x+iy)}\pm N$ for some large $N$ projected onto the $xz$-plane? I would imagine that if we found any asymptotes converging anywhere other than ...
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### Will Riemann Hypothesis, if true, give us the exact value of number of primes less than a given number?

As we know that RH is the most popular unsolved problem in all of maths. If this hypothesis is true, then will it give us the power to predict the exact number of primes less then a given number? And ...
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### On the series $\sum_{n=1}^{\infty} (H_{n}+\exp(H_{n})\log(H_{n}))/n^{s}$, where $H_{n}$ is the $n$th harmonic number

It is known the following (see [1], here is an open access PDF on his homepage): Theorem (Lagarias, 2002). Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Riemann Hypothesis ...
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### Are there papers or books that explain why Bernhard Riemann believed that his hypothesis is true?

I would like to know what are the mathematical reasons for which Bernhard Riemann believed that his hypothesis is true, and I would like to know if those mathematical reasons were cited in his ...
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### Riemann hypothesis reformulation - again

Yesterday I started to write a paper about the reformulation of the Riemann Hypothesis. My idea was to map the function such that all of the trivial zeros are outside of the unit disk, and the non-...
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### What are the most promising approches for solving Riemann hypothesis? [closed]

I'm not a mathematician but still I'm very interested in Riemann hypothesis. I discovered it with the Numberphile channel. I would like to know what are the current work done of this subject and if ...
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### Bibilography: Riemann's hypothesis and positive semi-definite billinear forms

This is a bibliography request: I remember browsing through a book, some years ago, in a library, in which Riemann's hypothesis was proved over some type of fields (I cannot remember what type), the ...
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### What is general Riemann's Hypothesis? [duplicate]

What makes it so important in analytic number theory?
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### Can $\zeta(s)$ be written in the form $\zeta(s)=\Re(\zeta(s))+i·\Im(\zeta(s))$ for some subset of $\mathbb{C}$?

Can $\zeta(s)$ be written in the form $\zeta(s)=f(s)+g(s) i$ for some subset of $\mathbb{C}$? I mean, is it possible to develop at least one of the formulas of $\zeta(s)$ so you get something like... ...