Irreducibility conjecture for random Rademacher polynomials

Let g±1,d(x)=xd+ad1xd1++a0g_{\pm1,d}(x)=x^d+a_{d-1}x^{d-1}+\dots+a_0 be a monic polynomial of positive degree dd, where each aia_i is independently +1+1 or 1-1 with probability 12\frac{1}{2}. Rademacher irreducibility conjecture. The probability that g±1,d(x)g_{\pm1,d}(x) is reducible goes to 00 as dd goes to infinity. The source presents this as the analogue, for coefficients in {+1,1}\{+1,-1\}, of the Odlyzko–Poonen conjecture; the preceding results give lower bounds for odd degrees from linear factors.

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Primary source

Christian Borst, Evan Boyd, Claire Brekken, Samantha Solberg, Melanie Matchett Wood and Philip Matchett Wood, “Irreducibility of Random Polynomials”, arXiv:1705.03709 (2017).

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