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Mean Value for Random Ideal Lattices: Lean formalization

Nihar Gargava

Palomar Registrypalomar/PALOMAR-2026-09-02-000009Sep 2, 2026math.NTscore 0

A Lean formalization of the geometric, analytic, and arithmetic argument for mean values of lattice-point counts in Haar-random unit-covolume ideal lattices. For cyclotomic fields, it proves the conditional quantitative estimate for every exponent below the assumed subconvexity exponent and its positive power-saving corollary, uniformly over origin-centered balls. The subconvexity, Stark residue, and discriminant-growth inputs remain explicit hypotheses rather than claimed consequences of the formalization.

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