Assuming there are infinitely many twin primes, one can consider a Dirichlet series $ \sum_{n>0}a_{n}{n^{-s}} $ and replace the sequence of positive integers with the sequence of twin primes. That way such a "twin prime transform" of the Riemann zeta function would give for $ s=1 $ the so called Brun constant.

What would thus be the abscissa of convergence for such a series assuming the original one is $ 1 $?