8:18 AM
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Let $f(n)=(1 + (-1)^{1 + n})/2$ (which gives 1, 0, 1, 0 ... as n increases from 1 on) and $\lambda(n)$ be the Liouville lambda function. Can I compute a Dirichlet series for $f(n)\lambda(n)$? I could not find it in the Gould and Shonhiwa catalog of known Dirichlet series, but I am convinced it mu...

In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Peter Gustav Lejeune Dirichlet. == Definition == If f , g : N → C {\displaystyle f,g:\mathbb {N} \to \mathbb {C} } are two arithmetic functions from the positive integers to the complex numbers, the Dirichlet convolution f ∗ g is a new arithmetic function defined by: ( f ∗...

6 hours later…
2:35 PM
A question with a deprecated tag was bumped - what would be a good replacement for ? Bounding the entropy of a convolution
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Say we have a function $f:\mathbb{Z}_2^n \to \mathbb{R}$, such that $\sum _{x\in \mathbb{Z}_2^n} f(x)^2 = 1$ (so we can think of $\{ f(x)^2\} _{x\in \mathbb{Z}_2^n}$ as a distribution). It is natural to define the entropy of such function $f$ as follows: H(f) = -\sum _{x \in \mathbb{Z}_2^n} f(x...

2 hours later…
4:56 PM
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The example I first learned was the following: a 2-D TQFT is equivalent to a Frobenius algebra. This is discussed and stated as a folk theorem by Voronov; later, a careful proof was written up and published by Lowell Abrams. See also the book by Joachim Kock.

The post contains this link: xxx.lanl.gov/abs/hep-th/9401023 - does somebody know how can the xxx.lanl.gov links be replaced to get working links. I do not see this domain listed here: Domains with dead links.
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In this post, Justin gives a quote about Raoul Bott that has this line in it: He talked about 'folk' theorems... theorems everyone knew, but were never written down. What are some good/interesting examples of these types of theorems?

A temporary comment - to update the list of linked posts: Folk Functorial Figuring. — Martin Sleziak 1 min ago
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In category theory there is a 'folk' model structure on the category Cat, where the weak equivalences are the equivalences of categories. There is a similar model structure on 2Cat, with weak equivalences being equivalences of 2-categories (weak ones, I presume) The former was not written down fo...