Double roots of random littlewood polynomials.

We consider random polynomials whose coefficients are independent and uniform on {-1, 1}. We prove that the probability that such a polynomial of degree n has a double root is o( n ) when n+1 is not divisible by 4 and asymptotic to $$1/\sqrt 3 $$ otherwise. This result is a corollary of a more general theorem that we prove concerning random polynomials with independent, identically distributed coefficients having a distribution which is supported on {-1, 0, 1} and whose largest atom is strictly less than $$\frac{{8\sqrt 3 }}{{\pi {n^2}}}$$ . In this general case, we prove that the probability of having a double root equals the probability that either -1, 0 or 1 are double roots up to an o( n ) factor and we find the asymptotics of the latter probability. [ABSTRACT FROM AUTHOR]