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

D. A.N. Carmon; Alexei Entin

doi:10.1017/S0305004119000392

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

D. A.N. Carmon, Alexei Entin

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the density of square-free values of polynomials with large coefficients over the rational function field 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 k-th power of a small polynomial and a square-free polynomial.

Original language	English
Pages (from-to)	247-263
Number of pages	17
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	170
Issue number	2
DOIs	https://doi.org/10.1017/S0305004119000392
State	Published - Mar 2021

Keywords

2010 Mathematics Subject Classification: 11N25 11N32 11N36 11R58 14H05

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004119000392

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abstract = "We investigate the density of square-free values of polynomials with large coefficients over the rational function field 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 k-th power of a small polynomial and a square-free polynomial.",

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AB - We investigate the density of square-free values of polynomials with large coefficients over the rational function field 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 k-th power of a small polynomial and a square-free polynomial.

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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