2015/06/16 by Men-Jaw Ho, Ho, Men-Jaw, Chou-Jung Hsu +3
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.1506.05335
openalex publication_date 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For integers x and k, let T(x;2k) denote the number of twin prime pairs (p,p+2k) with a distance 2k<=2x**0.5 and p<=x (not p+2k<=x). Let Tg(x;2x**0.5) denote the average of T(x;2k) for all 2k<=2x**0.5. Logically, T(x;2k) should be a function of Tg(x;2x**0.5). We first, propose a sliding model to estimate Tg(x;2x**0.5). Second, derive the relations between T(x;2k) and Tg(x;2x**0.5) from the sieve structure. Third, settle the errors caused by the dependence of primes.