Approximating reals by sums of rationals

2007/04/20 by Chan, Tsz Ho
#11J04 #11L07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0704.2805

Abstract

We consider the question of approximating any real number α by sums of n rational numbers (a₁)/(q₁) + (a₂)/(q₂) + ... + (a_n)/(q_n) with denominators 1 ≤ q₁, q₂, ..., q_n ≤ 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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