Ramanujan inspired p series deformation for gravitational modeling across newtonian and cosmic scales

This preprint presents an analytic deformation of classical p-series inspired by Ramanujan-type constructions, leading to a rapidly convergent kernel with controlled asymptotic behavior. The kernel admits explicit normalization, Mellin-type integral representations, and well-defined scaling limits, allowing it to be employed as a smooth, scale-dependent modification of Newtonian gravitational modeling without altering its leading inverse-square structure.

Rigorous analysis of convergence, asymptotic regimes, and parameter dependence is provided, establishing the mathematical consistency of the framework across short- and long-distance scales. The resulting formulation is intended as a phenomenological and analytically controlled modeling tool rather than a new fundamental physical law. Potential applications to gravitational systems across Newtonian and cosmological scales are discussed within a mathematically well-posed setting.