Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Sparse squares of polynomials


Author: John Abbott
Journal: Math. Comp. 71 (2002), 407-413
MSC (2000): Primary 11C04; Secondary 12Y05
Published electronically: October 17, 2000
MathSciNet review: 1863010
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

We answer a question left open in an article of Coppersmith and Davenport which proved the existence of polynomials whose powers are sparse, and in particular polynomials whose squares are sparse (i.e., the square has fewer terms than the original polynomial). They exhibit some polynomials of degree $12$ having sparse squares, and ask whether there are any lower degree complete polynomials with this property. We answer their question negatively by reporting that no polynomial of degree less than $12$ has a sparse square, and explain how the substantial computation was effected using the system CoCoA.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11C04, 12Y05

Retrieve articles in all journals with MSC (2000): 11C04, 12Y05


Additional Information

John Abbott
Affiliation: Dipartimento di Matematica, Università di Genova, Italy
Email: abbott@dima.unige.it

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01294-1
PII: S 0025-5718(00)01294-1
Received by editor(s): February 1, 2000
Published electronically: October 17, 2000
Article copyright: © Copyright 2000 American Mathematical Society