An Arithmetic Defect beyond the Symplectic Trace Wall

Abstract

We study the fixed-distance range beyond the symplectic trace wall for quadratic L-functions over function fields. Using Wang's ratios theorem and a four-swap calculation, we identify an arithmetic Euler factor in the limiting second moment. For distance three, the first correction is 2/q^3 + O(q^-4), disproving universal post-wall saturation for all sufficiently large fixed odd prime powers. We also define the stable Euler coefficient for every fixed odd prime power and give a rigorous interval computation at q=3.