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Zbl 1066.11030
Waldschmidt, Michel
Open Diophantine problems. (English)
[J] Mosc. Math. J. 4, No. 1, 245-305 (2004). ISSN 1609-3321

\par This paper gives a very detailed survey of the most important conjectures and problems in Transcendental Number Theory and Diophantine Approximation. Its 61 pages contain a lot of information. It is almost impossible to give a complete review of it, I shall only present a list of the main topics treated in this survey. The different sections are: 1. Diophantine equations 2. Diophantine Approximation 3. Transcendence 4. Heights 5. Further Problems: Metric Problems, Function Fields. The paper contains more than 70 problems or conjectures. This is a splendid road-map for the present millenium.
[Maurice Mignotte (Strasbourg)]

MSC 2000:: *11Jxx Diophantine approximation
11-02 Research monographs (number theory)
11Dxx Diophantine equations
11G50 Heights
14G05 Rationality questions, rational points

Keywords: Transcendental number theory; Diophantine approximation; Diophantine equations

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