# Open Diophantine problems

@inproceedings{Waldschmidt2001OpenDP, title={Open Diophantine problems}, author={Michel Waldschmidt}, year={2001} }

Diophantine Analysis is a very active domain of mathemat- ical research where one finds more conjectures than results. We collect here a number of open questions concerning Diophantine equations (including Pillai's Conjectures), Diophantine approximation (featuring the abc Conjecture) and transcendental number theory (with, for instance, Schanuel's Conjecture). Some questions related to Mahler's measure and Weil absolute logarithmic height are then considered (e.g., Lehmer's Problem). We also…

## 62 Citations

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. We prove a Diophantine approximation inequality for rational points in varieties of any dimension, in the direction of Vojta’s conjecture with truncated counting functions. Our results also provide…

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### Metric Diophantine Approximation : aspects of recent work

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