Irreducibility of random reciprocal polynomials

Organisé par

Institut Henri Poincaré

Let $P = a_m T^m + \sum_{j=0}^{m} a_j (T^{m-j} + T^{m+j})$ be a monic reciprocal polynomial of even degree n, with the $a_j$ drawn independently and uniformly at random from $\{1, 2, \ldots, H\}$ for some fixed integer $H \geq 35$. In joint work with Dimitris Koukoulopoulos, building on prior work of Bary-Soroker—Koukoulopoulos—Kozma, we show that $P$ is irreducible over the rationals, and has lar

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