Over on the polymath blog, I’ve posted (on behalf of Dinesh Thakur) a new polymath proposal, which is to explain some numerically observed identities involving the irreducible polynomials in the polynomial ring over the finite field of characteristic two, the simplest of which is

(expanded in terms of Taylor series in ). Comments on the problem should be placed in the polymath blog post; if there is enough interest, we can start a formal polymath project on it.

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28 December, 2015 at 9:59 pm

Gil KalaiThis looks like a very nice project! If it will be developed into a full project this will be (I think) the first time that we have more than one polymath project running in parallel and this is very welcomed! Right now polymath10 devoted to the Erdos-Rado sunflower conjecture is running in my blog; Here is the link to the first post. It is quite possible that yet another polymath project will take place over a third blog in the coming months.

29 December, 2015 at 5:27 am

Gil KalaiOne more general polymath news: Here is the link of a mathoverflow question asking for polymath proposals http://mathoverflow.net/questions/219638/proposals-for-polymath-projects

29 December, 2015 at 8:07 am

AnonymousIt seems to involve the Carlitz zeta function. Is there any introductory material on that topic?

29 December, 2015 at 2:16 pm

AnonymousAlso, Prof. Tao, is it a good idea to make a “reference request” on mathoverflow about Carlitz zeta functions so that we could have more reference?

30 December, 2015 at 8:21 am

David SpeyerGoss’s book is a good quick reference.

30 December, 2015 at 5:52 pm

Anonymousso it seems done, right?

29 December, 2015 at 10:09 am

John MangualAt first I thought of Turán’s Sieve, but then I learned the irreducible polynomials can be counted by inclusion-exclusion: http://math.stackexchange.com/questions/40811/number-of-monic-irreducible-polynomials-of-degree-p-over-finite-fields

What else…? Plug in etc or something very close.