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An isoperimetric inequality related to Thue's equation
Author(s):
Michael A.
Bean
Journal:
Bull. Amer. Math. Soc.
31
(1994),
204-207.
MathSciNet review:
1260516
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
This paper announces the discovery of an isoperimetric inequality for the area of plane regions defined by binary forms. This result has been applied subsequently in the enumeration of solutions to the Thue inequality and, given its fundamental nature, may find application in other areas as well.
References:
-
- [1]
- M. Abramowitz and I. Stegun, Handbook of mathematical functions, Dover, New York, 1965.
- [2]
- M. A. Bean, Areas of plane regions defined by binary forms, Ph.D. thesis, Univ. of Waterloo, 1992.
- [3]
- -, Binary forms, hypergeometric functions, and the Schwarz-Christoffel mapping formula, submitted.
- [4]
- -, An isoperimetric inequality for the area of plane regions defined by binary forms, Compositio Math. (to appear). MR 1283225 (95i:11078)
- [5]
- M. A. Bean and J. L. Thunder, Isoperimetric inequalities for volumes associated with decomposable forms, submitted.
- [6]
- G. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952. MR 0046395 (13:727e)
- [7]
- K. Mahler, Zur Approximation algebraischer Zahlen III, Acta Math. 62 (1934), 91-166. MR 1555382
- [8]
- J. Mueller and W. M. Schmidt, On the Newton polygon, Monatsh. Math. 113 (1992), 33-50. MR 1149059 (93f:12003)
- [9]
- -, Thue's equation and a conjecture of Siegel, Acta Math. 160 (1988), 207-247. MR 945012 (89g:11029)
- [10]
- W. M. Schmidt, Diophantine approximations and diophantine equations, Lecture Notes in Math., vol. 1467, Springer-Verlag, New York, 1991. MR 1176315 (94f:11059)
- [11]
- A. Thue, Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135 (1909), 284-305.
- [12]
- J. L. Thunder, The number of solutions to cubic Thue inequalities, Acta Arith. (to appear). MR 1276991 (95e:11042)
Additional Information:
DOI:
10.1090/S0273-0979-1994-00517-8
PII:
S 0273-0979(1994)00517-8
Copyright of article:
Copyright
1994,
American Mathematical Society
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