On square-free values of large polynomials over the rational function field

2016/05/25 by Dan Carmon, Carmon, Dan, Alexei Entin +1
Mathematics · #11T55 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1605.07765

openalex publication_date 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We investigate the density of square-free values of polynomials with large coefficients over the rational function field \mathbbF_q[t]. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial N as a sum of a small k-th power and a square-free polynomial.

Related

• Square-free values of polynomials evaluated at primes over a function field
• Squarefree values of polynomials over the rational function field
• Squarefree density of polynomials
• Square-free values of multivariate polynomials over function fields in\n linear sparse sets
• Density of power-free values of polynomials II