2011/08/18 by Adam J. Harper, Harper, Adam J.
Engineering · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems #math.NT
paper · pdf · doi:10.48550/arxiv.1108.3819
32 pages
arxiv created 2011/08/18 · openalex publication_date 2011/08/18 · arxiv updated 2011/08/19 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
We give improved lower bounds for the number of solutions of some S-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method is quite conceptually straightforward, although its successful implementation involves, amongst other things, a slightly subtle use of a large sieve inequality. We also present two other results about solving linear equations on average over their coefficients.