2011/07/29 by Chaohua Jia, Jia, Chaohua
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1107.6039
arxiv created 2011/07/29 · openalex publication_date 2011/07/29 · arxiv updated 2011/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the positive integer n, let f(n) denote the number of positive integer solutions (n1, n2, n3) of the Diophantine equation 4\over n=1\over n1+1\over n2+1\over n3. For the prime number p, f(p) can be split into f1(p)+f2(p), where fi(p)(i=1, 2) counts those solutions with exactly i of denominators n1, n2, n3 divisible by p. Recently Terence Tao proved that ∑p< xf1(p)≪ xexp(clog x\over loglog x) with other results. In this paper we shall improve it to ∑p< xf1(p)≪ xlog5xloglog2x.