On the nearest irreducible lacunary neighbour to an integer polynomial

Bera, Ranjan and Banerjee, Pradipto (2020) On the nearest irreducible lacunary neighbour to an integer polynomial. Colloquium Mathematicum, 162 (1). pp. 121-134. ISSN 0010-1354

Full text not available from this repository. (Request a copy)

Abstract

There is an absolute constant D0 > 0 such that if f(x) is an integer polynomial, then there is an integer λ with |λ| ≤ D0 such that xn + f(x) + λ is irreducible over the rationals for infinitely many integers n ≥ 1. Furthermore, if deg f ≤ 25, then there is a λ with λ ∈ {−2, −1, 0, 1, 2, 3} such that xn + f(x) + λ is irreducible over the rationals for infinitely many integers n ≥ 1. These problems arise in connection with an irreducibility theorem of Andrzej Schinzel associated with coverings of integers and an irreducibility conjecture of Pál Turán.

[error in script]
IITH Creators:
IITH CreatorsORCiD
Bera, RanjanUNSPECIFIED
Banerjee, PradiptoUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: irreducible polynomial; Turán’s problem
Subjects: Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 06 Aug 2021 10:21
Last Modified: 06 Aug 2021 10:21
URI: http://raiith.iith.ac.in/id/eprint/8716
Publisher URL: http://doi.org/10.4064/cm7978-8-2019
OA policy: https://v2.sherpa.ac.uk/id/publication/14741
Related URLs:

Actions (login required)

View Item View Item
Statistics for RAIITH ePrint 8716 Statistics for this ePrint Item