Simultaneous approximation of additive forms

Liu, Ming Chit

doi:10.1090/S0002-9947-1975-0366820-7

Simultaneous approximation of additive forms
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Trans. Amer. Math. Soc. 206 (1975), 361-373 Request permission

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 $||{f_i}(X)||$, where $||t||$ means the distance from $t$ to the nearest integer.

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Vorlesungen über Zahlentheorie

Elementary number theory

19

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