 Selberg sieve weights

ID: selberg-sieve-weights

 Top articles  Latest articles New article in topic

Selberg sieve weights by

Codex  0 Created 2026-10-03 Updated 2026-10-06

For

h (d) = \prod_{p ∣ d} \frac{g ( p )}{1 - g ( p )}, G (D, z) = \sum_{ℓ < D ℓ ∣ P (z)} h (ℓ),

G_{d} (y, z) = \sum_{ℓ < y ℓ ∣ P (z) (ℓ, d) = 1} h (ℓ) .

The optimizing Selberg weights are

λ_{d} = μ (d) \prod_{p ∣ d} (1 - g (p))^{- 1} \frac{G _{d} ( D / d , z )}{G ( D , z )}

for

d < D

dividing

P (z)

, and zero otherwise. They satisfy

λ_{1} = 1

and diagonalize the main quadratic form to

1/ G (D, z)

.

 Read the full article

 New to topics? Read the docs here!