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Employing the Bogoliubov coefficient summation method and introducing thegyromagnetic ratio $g\neq 2$ we derive an explicit functional form of$\mathfrak{Im}V^\mathrm{EHS}_g$, the imaginary part ofEuler-Heisenberg-Schwinger (EHS) type effective action. We show that$\mathfrak{Im}V^\mathrm{EHS}_g$ is periodic in $g$ for any (quasi-)constantelectromagnetic field configuration, and equal to the imaginary part obtainedusing a periodic in $g$ Ramanujan integrand in the proper time representationof $V^\mathrm{EHS}_g$. This validates the Ramanujan representation of$V^\mathrm{EHS}_g$ for both real and imaginary parts and allows writing theeffective action in a suitably modified Schwinger proper time format. As afunction of the ratio $b/a$ between ${\mathcal{B}} \to b$ and ${\mathcal{E}}\toa$ covariant generalizations of EM fields, we explore the singular propertiesof $\mathfrak{Im}V^\mathrm{EHS}_g$ at $g=2\pm 4k, k=0,\pm1,\pm2\ldots$involving the pseudoscalar $ab\equiv \vec{\mathcal{E}}\cdot\vec{\mathcal{B}}$in perturbative and nonperturbative behavior. We study the $e^-e^+$-decayvacuum instability, incorporating the physical value of $g-2$ vertex diagramswhen summing infinite irreducible loops. We obtain an effective expansionparameter $\chi_b=\alpha b/2a$ ($\alpha=e^2/4\pi$), characterizing the onset ofnonperturbative in $g-2$ suppression of vacuum instability. We demonstrate the$\chi_b$ domains for which perturbative expansion in $\alpha$ breaks down: TheEM vacuum subject to critical electric field strength is stabilized inmagnetic-dominated \lq magnetar\rq\ environments. Considering separately thecase of ${\mathcal{E}}$ and ${\mathcal{B}}$ fields, we generalize to all $g$the temperature representation of the $V^\mathrm{EHS}_g$ effective action.

Singular properties of QED vacuum response to applied quasi-constant electromagnetic fields