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arXiv · 0704.2805

Approximating reals by sums of rationals

Tsz Ho Chan
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Abstract

We consider the question of approximating any real number $α$ by sums of $n$ rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2} + ... + \frac{a_n}{q_n}$ with denominators $1 \leq q_1, q_2, ..., q_n \leq N$. This leads to an inquiry on approximating a real number by rational numbers with a prescribed number of prime factors in the denominator.

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Tsz Ho Chan. 2007-04-20. Approximating reals by sums of rationals. https://arxiv.org/abs/0704.2805

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