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Büchi Sequences in Local Fields and Local Rings

Jerzy Browkin (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring $ℤ_{p}$ of p-adic integers. In $ℤ_{p}$ there are only finite but arbitrarily long Büchi sequences.

Büchi's problem in any power for finite fields

Hector Pasten (2011)

Acta Arithmetica

Buck's measure density and sets of positive integers containing arithmetic progression

Milan Paštéka, Tibor Šalát (1991)

Mathematica Slovaca

Burnside's uniformization

R. A. Rankin (1997)

Acta Arithmetica

BV coboundaries over irrational rotations

Dalibor Volný (1997)

Studia Mathematica

For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.