3 problems

Define the weighted Goldbach representation function … and the singular series … where $C_2$ is the twin prime constant. Friedlander–Goldston–Iwaniec–Suriajaya conjecture. There ex…

Let $R(n)$ denote the number of representations of an integer $n$ as a sum of two primes, and let $\varphi$ denote Euler's totient function. Jia's strengthened Hardy–Littlewood con…

Let $R(n)$ denote the number of representations of an integer $n$ as a sum of two primes. Weak Hardy–Littlewood conjecture. There exists an absolute constant $c_3>0$ such that, for…