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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.
MSC (1991):
Primary 11D75, 11J25, 51M25;
Secondary 26D20, 33B15
MathSciNet review:
1260516
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Additional information
References:
- [1]
- M. Abramowitz and I. Stegun, Handbook of mathematical functions, Dover, New York, 1965. MR
- [2]
- M. A. Bean, Areas of plane regions defined by binary forms, Ph.D. thesis, Univ. of Waterloo, 1992. MR
- [3]
- M. A. Bean, Binary forms, hypergeometric functions, and the Schwarz-Christoffel mapping formula, submitted. MR
- [4]
- M. A. Bean, An isoperimetric inequality for the area of plane regions defined by binary forms, Compositio Math. MR 1283225
- [5]
- M. A. Bean and J. L. Thunder, Isoperimetric inequalities for volumes associated with decomposable forms, submitted. MR
- [6]
- G. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952. MR 46395
- [7]
- K. Mahler, Zur Approximation algebraischer Zahlen \rm {III}, Acta Math. \textbf{62} (1934), 91--166. MR 1555382
- [8]
- J. Mueller and W. M. Schmidt, On the Newton polygon, Monatsh. Math. \textbf{113} (1992), 33--50. MR 1149059
- [9]
- J. Mueller and W. M. Schmidt, Thue\RM 's equation and a conjecture of Siegel, Acta Math. \textbf{160} (1988), 207--247. MR 945012
- [10]
- W. M. Schmidt, Diophantine approximations and diophantine equations, Lecture Notes in Math., vol.~1467, Springer-Verlag, New York, 1991. MR 1176315
- [11]
- A. Thue, \"Uber Ann\"aherungswerte algebraischer Zahlen, J. Reine Angew. Math. \textbf{135} (1909), 284--305. MR
- [12]
- J. L. Thunder, The number of solutions to cubic Thue inequalities, Acta Arith. MR 1276991
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Additional Information:
DOI:
10.1090/S0273-0979-1994-00517-8
PII:
S 0273-0979(1994)00517-8
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