An explicit polynomial analogue of Romanoff's theorem

Igor E. Shparlinski*, Andreas J. Weingartner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given a polynomial g of positive degree over a finite field, we show that the proportion of polynomials of degree n, which can be written as h+gk, where h is an irreducible polynomial of degree n and k is a nonnegative integer, has order of magnitude 1/deg⁡g.

Original languageEnglish
Pages (from-to)22-33
Number of pages12
JournalFinite Fields and their Applications
Volume44
DOIs
Publication statusPublished - 1 Mar 2017
Externally publishedYes

Keywords

  • Irreducible polynomial
  • Multiplicative order
  • Polynomial ring
  • Romanoff's theorem

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