The Asymptotic Spectral Phase-Lock: Uniform Conformal Convergence of Automorphic L-Functions at the Infinite Boundary

This paper introduces a localized conformal coordinate transformation designed toevaluate the asymptotic distribution of zeros of the Riemann Zeta function ζ(s) along thecritical line. By mapping this transformation to the boundary of a unitary Degree 2 Maasscusp form at the infinite cusp (y → ∞), we analyze the simultaneous interaction of thegeometric Whittaker decay and the logarithmic phase acceleration. We prove that undera coupled trajectory, the exponential decay O(e−2πy) uniformly dominates the logarithmicscaling factor, causing all residual error terms to vanish identically at the limit point. Thisestablishes a localized spectral phase-lock at the infinite horizon, offering a new geometricframework for asymptotic zero confinement.