Let $F(\sigma+it)=\sum_{n=1}^{\infty}a_n n^{-(\sigma+it)}$ a Dirichlet series that is absolutely convergent in the half-plane $\sigma>\sigma_a$ and let $G(\sigma+it)$ be a function such that $$F(\sigma)=G(\sigma),$$ for all $\sigma>\sigma_a$.

In this general setting is it true that $F(\sigma+it)=G(\sigma+it)$, in the half-plane $\sigma>\sigma_a$?

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    $\begingroup$ What do a know about $G$? $\endgroup$ – Kavi Rama Murthy Apr 4 at 10:29
  • $\begingroup$ @KaviRamaMurthy it is a product of a Dirichlet series with an integral depending on this same DS. $\endgroup$ – GoldSoundz Apr 4 at 10:33

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