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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For an odd positive integer 
, assuming the truth of the 
conjecture, we show that for a positive proportion of pairs 
of integers the trinomials of the form 
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
