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On pairs of additive forms modulo one
Published online by Cambridge University Press: 24 October 2008
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