@article{17127,
abstract = {Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation
∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0
(for any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as N→+∞
, where f is the Steinhaus random multiplicative function.},
author = {Wang, Victor and Xu, Max Wenqiang},
issn = {1469-2120},
journal = {Bulletin of the London Mathematical Society},
publisher = {London Mathematical Society},
title = {{Paucity phenomena for polynomial products}},
doi = {10.1112/blms.13095},
year = {2024},
}