The paper is being retracted by the author due to an erratum in the application of Grosswald’s result on the existence of $m_G(s)$, which invalidates the proof of Theorem 2.
"[RETRACTED] On Hilbert’s 8th problem." Braz. J. Probab. Stat. 32 (3) 670 - 678, August 2018. https://doi.org/10.1214/18-BJPS392