Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Finite Mixed Weil Majorant

Abstract

All mixed convolution terms of a finite Weil basis are absolutely summable and yield one majorant uniform over the whole coefficient space.

Theorem 1.1 (The square includes every coefficient cross term).

Lean statement: D5/S3/Weil/BurnolGram/FiniteMixedWeilMajorant.zeroSummand_finite_synthesis_expansion

Proof. Machine-checked in Lean as D5/S3/Weil/BurnolGram/FiniteMixedWeilMajorant.zeroSummand_finite_synthesis_expansion (✓ std3). ∎

Source. Repository-derived.

Commentary.

The mixed summand is the actual zero summand of convolve(g_i,involution(g_j)), so its absolute summability comes from the existing zeta explicit formula. No diagonal-only estimate is substituted for a bound on the full family.

Theorem 1.2 (One fixed majorant controls every coefficient vector).

Lean statement: D5/S3/Weil/BurnolGram/FiniteMixedWeilMajorant.finite_synthesis_absolute_sum_le

Proof. Machine-checked in Lean as D5/S3/Weil/BurnolGram/FiniteMixedWeilMajorant.finite_synthesis_absolute_sum_le (✓ std3). ∎

Source. Repository-derived.

Commentary.

Each coefficient product has norm at most the complete coefficient energy. Summing all mixed absolute terms gives a finite constant independent of the coefficient vector and of later convolution-power depth.

References