Tilings of the Integers, Vanishing Sums of Roots of Unity, and Cyclotomic Arrays
نویسنده
چکیده
The thesis explores three different topics: tilings of the integers, vanishing sums of roots of unity, and cyclotomic arrays, which are all closely intertwined. On tilings of the integers, we prove two existence results for level semigroups and three different lower bounds on tiling periodicities. On vanishing sums of roots of unity, we solve an open problem of H.W. Lenstra [33]. On cyclotomic arrays we give the proof of a result of ours and Don Coppersmith [11] on nonnegative integer linear combinations, which generalizes a result of Lam and Leung [31].
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