Corollary 1: short sums in arithmetic progressions

def NairTenenbaum.CorollaryOne : Prop

Corollary 1 with the coefficient-height threshold independent of β, the arithmetic growth exponent εβδ/6, and both omitted-prime restrictions in the main term. As in Theorem 1, the irreducible factorization data are supplied.

Equations

• One or more equations did not get rendered due to their size.

theorem NairTenenbaum.corollaryOne : CorollaryOne

Proof of Corollary 1. The argument retains the original scale after affine substitution and uses the exact transformed weight and Euler-product identities.