2011/09/05 by Chaohua Jia, Jia, Chaohua
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1109.0867
arxiv created 2011/09/05 · openalex publication_date 2011/09/05 · arxiv updated 2011/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For given positive integers n and a, let R(n; a) denote the number of positive integer solutions (x, y) of the Diophantine equation a\over n=1\over x+1\over y. Write S(N; a)=∑_\substackn≤ N (n, a)=1R(n; a). Recently Jingjing Huang and R. C. Vaughan proved that for 4≤ N and a≤ 2N, there is an asymptotic formula S(N; a)=3\over π2a∏p|ap-1\over p+1⋅ N(log2N+c1(a) log N+c0(a))+Δ(N; a). In this paper, we shall get a more explicit expression with better error term for c0(a).