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Counting squarefree discriminants of trinomials under abc


Authors: Anirban Mukhopadhyay, M. Ram Murty and Kotyada Srinivas
Journal: Proc. Amer. Math. Soc. 137 (2009), 3219-3226
MSC (2000): Primary 11R09; Secondary 11C08
DOI: https://doi.org/10.1090/S0002-9939-09-09831-1
Published electronically: June 8, 2009
MathSciNet review: 2515392
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Abstract: For an odd positive integer $ n\ge 5$, assuming the truth of the $ abc$ conjecture, we show that for a positive proportion of pairs $ (a,b)$ of integers the trinomials of the form $ t^n+at+b \ (a,b\in \mathbb{Z})$ are irreducible and their discriminants are squarefree.


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Additional Information

Anirban Mukhopadhyay
Affiliation: Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai 600 113, India
Email: anirban@imsc.res.in

M. Ram Murty
Affiliation: Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
Email: murty@mast.queensu.ca

Kotyada Srinivas
Affiliation: Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai 600 113, India
Email: srini@imsc.res.in

DOI: https://doi.org/10.1090/S0002-9939-09-09831-1
Keywords: Irreducible polynomials, squarefree discriminants, quadratic extensions
Received by editor(s): August 5, 2008
Published electronically: June 8, 2009
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society

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