Counting (skew-)reciprocal Littlewood polynomials with square discriminant
Abstract
Abstract A Littlewood polynomial is a univariate polynomial all of whose coefficients lie in {±1}. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant. This relates to a bounded-height analogue of the Van der Waerden conjecture on Galois groups of random polynomials. As a byproduct, we establish the asymptotics of certain Gaussian-weighted counts of Pythagorean triples.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Geometry and complex manifolds
Advanced Algebra and Geometry
Publication details
- Journal / source
- Israel Journal of Mathematics
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 6 April 2026
- Language
- EN