Uri Shapira (Hebrew University)
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A solution to an open problem of Cassels and Diophantine
properties of cubic numbers.

The abstract is: 
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Abstract: We prove existence of real numbers x,y, possessing
the following property:
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For any real a,b, liminf  |n| ||nx - a|| ||ny - b|| = 0,
where ||c|| denotes the distance of c to the nearest integer.
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This answers a 50 years old question of Cassels.
The most interesting part of the result is that there are algebraic
numbers with the above property!



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