Approximation by Several Rationals

2007/07/23 by Igor E. Shparlinski, Shparlinski, Igor E.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.0707.3371

arxiv created 2007/07/23 · openalex publication_date 2007/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a₁/q₁, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible ranges for the denominators q₁,..., q_n, one can improve a result of T. H. Chan by using a different approach.

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