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On pairs of additive forms modulo one

Published online by Cambridge University Press:  24 October 2008

S. Schäffer
S. Schäffer
Affiliation:
Am Pastorenholz 8, 4972 Löhne, Germany
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Extract

Throughout this paper ∈ denotes an arbitrary positive number. For real α, ‖α‖ denotes the distance from α to the nearest integer. For natural numbers k we write K = 2k−1. In 1948 Heilbronn [8] showed that for any real α and N > C1(∈)

This theorem has since been generalized in many ways. In particular, results of the following type have been proved for natural numbers k ≥ 2, h = 1,2 and s.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 455 - 466
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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