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Short sums of certain arithmetic functions (Nair–Tenenbaum)

Jason Davies

Palomar Registrypalomar/PALOMAR-2026-10-30-000010Oct 30, 2026math.NTscore 0

A Lean 4 formalization of Nair and Tenenbaum's uniform upper bounds for short sums of nonnegative arithmetic functions evaluated at integer polynomial values. Theorem 1 retains the coefficient-independent height threshold and the restricted-discriminant dependence of the bound. Theorem 2 gives a greatest-prime-factor bound with a strict exponential gain for arbitrary nonconstant irreducible integer polynomials, including those with fixed prime divisors. Theorem 3 treats prime arguments with the explicit constant-term correction. The development also proves the ten corollaries on…

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