What is (chebyshev-function) tag for?

Question

When you look at questions currently tagged chebyshev-function, you will see questions from various areas there. (Number theory, Chebyshev polynomials, Chebyshev inequality,...) The tag-info for this tag is currently empty.

My first guess would be that this tag is supposed to be used for questions about Chebyshev functions such as $\vartheta(x)$ and $\psi(x)$, which are used in analytic number theory. (But there might be also some other meanings of this term I am unaware of.)

I think that it would be good to:

• Agree what this tag should be used for.
• Fill in the tag-excerpt and tag-wiki, explaining when the tag should be used.
• Clean up this tag. (Remove the tag from the questions belong there. Add the tag to the questions about Chebyshev functions.)
• If incorrectly tagged questions will keep appearing even after the tag-wiki is added, we might also create a comment template explaining correct usage of this tag.

But I wanted to get some input from other community members first.

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I searched a bit whether this tag has already been discussed here on meta. The only thing I found was a mention of this tag in this answer:

Cautionary tale: chebyshev-function is full of questions about Chebyshev-whatever, but not -function. At a glance, I have not found a single question about actual Chebyshev functions there. It is not unusual for rarely-used tags with few followers to degenerate into such a mess.

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EDIT: Since nobody objected to the idea that this tag - if we keep it - should only be for questions about Chebyshev functions in number theory, I went ahead and created tag-wiki and tag-exceprt.

I have also started retagging questions which do not belong here, see this list. They are mostly about Chebyshev polynomials and Chebyshev inequality. Since I am not very familiar with these two topics, some people with more experience in these areas might have a look at those questions and choose better tags, if needed.

Of course, if there is support for the suggestion to get rid of the tag entirely - as suggested in the AlexR's answer - this still can be done. (Although in that case we will have remove the tag-wiki, since the tags having tag-wiki are not removed from the system.)

Answer 1

Suggestion for the tag-info, in case we decide to keep the tag. (I made the post CW, feel free to make any reasonable improvements.)

Tag-excerpt:

For questions about Chebyshev functions $\vartheta(x)$ and $\psi(x)$, which are often used in number theory. For questions about Chebyshev polynomials, use the (chebyshev-polynomials) tag.

Tag-wiki:

This tag is intended for questions about Chebyshev functions $\vartheta(x)$ and $\psi(x)$, which are often used in number theory. These functions are defined as $$\vartheta(x)=\sum_{p\le x} \log p$$ and $$\psi(x) = \sum_{p^k\le x}\log p=\sum_{n \leq x} \Lambda(n) = \sum_{p\le x}\lfloor\log_p x\rfloor\log p.$$

For questions about Chebyshev polynomials, use the chebyshev-polynomials tag.

Answer 2

Those questions which really are about chebyshev-functions seem sufficiently tagged by analytic-number-theory, so maybe we should just soft-delete the tag (remove, don't blacklist).

I didn't see any question which would need retagging after removing chebyshev-function, but if we decide to keep it I suggest notifying about chebyshev-polynomials in the wiki since it seems one of the most common mistags.