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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Simultaneous approximation of additive forms


Author: Ming Chit Liu
Journal: Trans. Amer. Math. Soc. 206 (1975), 361-373
MSC: Primary 10F10
DOI: https://doi.org/10.1090/S0002-9947-1975-0366820-7
MathSciNet review: 0366820
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Abstract: Let $ X = ({x_1}, \cdots ,{x_s})$ be a vector of $ s$ real components and $ {f_i}(X) = \sum\nolimits_{j = 1}^s {{\theta _{ij}}x_j^k} (k = 2,3, \cdots ;i = 1, \cdots ,R) R$ additive forms, where $ {\theta _{ij}}$ are arbitrary real numbers. The author obtains some results on the simultaneous approximation of $ \vert\vert{f_i}(X)\vert\vert$, where $ \vert\vert t\vert\vert$ means the distance from $ t$ to the nearest integer.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0366820-7
Keywords: Additive form, Diophantine approximation, simultaneous approximation, asymptotic behaviour
Article copyright: © Copyright 1975 American Mathematical Society