On the boundedness of Weyl sums |
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| Authors: | Peter Hellekalek |
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| Institution: | (1) Institut für Mathematik, Universität Salzburg, Hellbrunner Straße 34, A-5020 Salzburg, Austria |
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| Abstract: | Leta be irrational and letf:0,1]  be Riemann-integrable with integral zero. Letf
n
(x) denote the Weyl sumf
n
(x):=
k=0
n–1
f({x
k >}),x /  0,1,n . We prove criteria for the boundedness of the sequence (f
n
)
n 1 and discuss the relation of this question to irregularities of the distribution of sequences. |
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| Keywords: | |
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