On the abscissas of a Dirichlet series and its subseries supported on prime factorization

Chaman Kumar Sahu

For a sequence $\{a_n{\}}_{n\ge 1}\subseteq (0,\infty )$ and a Dirichlet series $f(s)={\sum }_{n=1}^{\infty }{a}_n{n}^{-s},$ let ${\sigma }_a(f)$ denote the abscissa of absolute convergence of…