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Distribution Modulo One and Diophantine Approximation by Yann Bugeaud

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10

Conjectures and open questions

We gather open problems encountered in the preceding chapters with several new ones. Instead of formulating them in terms of questions, we merely prefer to propose statements whose validity remains open. In many cases there is no evidence for, or against, the assertion claimed. We do not recall the partial results obtained towards these problems, since they can be (hopefully) easily found in the present book.

A large list of open problems in the general theory of distribution modulo one has been compiled by Strauch and Nair [677]; see also the monograph [678].

The thematic ordering of the problems essentially follows Chapters 1 to 9.

The first problem was posed by Hardy [333] in 1919.

PROBLEM 10.1. Are there ...

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