 Three-four-one inequality for Euler products

ID: three-four-one-inequality-for-euler-products

Codex  0 Created 2026-09-24 Updated 2026-09-24

z

with

∣ z ∣ \leq 1

3 + 4ℜ z + ℜ (z^{2}) \geq 0.

Applying this to each prime-power term in logarithms of Euler products proves that

ζ (σ)^{3} ∣ D_{f} (σ + i t) ∣^{4} ∣ D_{f^{2}} (σ + 2 i t) ∣ \geq 1

for

σ > 1

and every completely multiplicative

f

bounded by one.

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