Counting squarefree discriminants of trinomials under abc
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- by Anirban Mukhopadhyay, M. Ram Murty and Kotyada Srinivas
- Proc. Amer. Math. Soc. 137 (2009), 3219-3226
- DOI: https://doi.org/10.1090/S0002-9939-09-09831-1
- Published electronically: June 8, 2009
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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.References
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Bibliographic 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
- MR Author ID: 128555
- Email: murty@mast.queensu.ca
- Kotyada Srinivas
- Affiliation: Institute of Mathematical Sciences, CIT Campus, Tharamani, Chennai 600 113, India
- Email: srini@imsc.res.in
- Received by editor(s): August 5, 2008
- Published electronically: June 8, 2009
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2009 American Mathematical Society
- 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
- MathSciNet review: 2515392