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Corvaja, P. and
Zannier, U. "A subspace theorem approach to integral points on curves", Compte Rendu Acad. Sci., 334, 2002, pp. 267–271
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226:'s method in diophantine approximation also is ineffective in describing possible very good rational approximations to almost all
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that depended only on the genus and not any special algebraic form of the equations. For
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Finitely many for a smooth algebraic curve of genus > 0 defined over a number field
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371:. Grundlehren der mathematischen Wissenschaften. Vol. 231. pp. 128–153.
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In 1929, Siegel proved the theorem unconditionally by combining a version of the
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in a given coordinate system, there are only finitely many points on
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In 1926, Siegel proved the theorem effectively in the special case
397:(1929). "Ăśber einige Anwendungen diophantischer Approximationen".
399:
Sitzungsberichte der
Preussischen Akademie der Wissenschaften
138:, so that he proved this theorem conditionally, provided the
256:. Siegel proved it effectively only in the special case
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in 1926. Effective results in some cases derive from
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gave a new proof by using a new method based on the
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161:(required in Weil's version, to apply to the
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337:. New Mathematical Monographs. Vol. 4.
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88:The theorem was first proved in 1929 by
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369:Elliptic curves: Diophantine analysis
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192:Siegel's result was ineffective for
36:Siegel's theorem on integral points
220:effective results in number theory
92:and was the first major result on
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335:Heights in Diophantine Geometry
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320:10.1016/S1631-073X(02)02240-9
100:> 1 it was superseded by
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339:Cambridge University Press
421:Theorems in number theory
333:; Gubler, Walter (2006).
151:diophantine approximation
147:Thue–Siegel–Roth theorem
70:with coordinates in the
249:{\displaystyle d\geq 5}
211:{\displaystyle g\geq 2}
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416:Diophantine equations
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94:Diophantine equations
18:Siegel's theorem
296:Diophantine geometry
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159:diophantine geometry
155:Mordell–Weil theorem
140:Mordell's conjecture
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395:Siegel, Carl Ludwig
275:{\displaystyle g=1}
131:{\displaystyle g=1}
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188:Effective versions
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102:Faltings's theorem
90:Carl Ludwig Siegel
38:states that for a
348:978-0-521-71229-3
228:algebraic numbers
16:(Redirected from
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64:affine space
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365:Lang, Serge
153:, with the
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32:mathematics
410:Categories
387:0388.10001
357:1130.11034
302:References
230:of degree
241:≥
222:), since
203:≥
172:In 2002,
142:is true.
104:in 1983.
367:(1978).
290:See also
85:> 0.
149:, from
108:History
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40:smooth
218:(see
157:from
50:genus
373:ISBN
343:ISBN
224:Thue
176:and
383:Zbl
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165:of
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270:1
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126:1
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120:g
98:g
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79:K
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60:K
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