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On the Distribution Modulo 1 of the Sequence αn2 + βn
Published online by Cambridge University Press: 20 November 2018
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Dirichlet's Theorem says that for any real α and for N ≧ 1, there exists a natural n ≦ N with
where || || denotes the distance to the nearest integer. Heilbronn [2], improving estimates of Vinogradov [3], showed that for α, N as above and for ϵ ≧ 0, there exists an n ≦ N with
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- Copyright © Canadian Mathematical Society 1977
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