Supersession history · C-0098

Fiori--Kadiri--Swidinsky's global absolute psi decay improves to 0.8817882

This lineage preserves 2 earlier results that led to the current listed result.

Superseded by C-0067 · C-0053 proved-unconditional

Fiori--Kadiri--Swidinsky's global absolute psi amplitude improves from 9.22022 to 9.2202181

For every real x>2, the absolute value of psi(x)-x is less than 9.2202181*x*(log x)^(3/2)*exp(-0.8476836*sqrt(log x)). This replaces the amplitude 9.22022 in Fiori--Kadiri--Swidinsky Corollary 1.4 while preserving its absolute-value formula, exponent, and full range.

Superseded by C-0098 · C-0067 proved-unconditional

Fiori--Kadiri--Swidinsky's global absolute psi decay improves to 0.88178

For every real x>2, |psi(x)-x| is less than 9.2202181*x*(log x)^(3/2)*exp(-0.88178*sqrt(log x)). This retains C-0053's amplitude and range while replacing the Fiori--Kadiri--Swidinsky decay 0.8476836 by 0.88178.

Current result · C-0098 proved-unconditional

Fiori--Kadiri--Swidinsky's global absolute psi decay improves to 0.8817882

For every real x>2, |psi(x)-x| is less than 9.2202181*x*(log x)^(3/2)*exp(-0.8817882*sqrt(log x)). This retains C-0067's amplitude and range while raising its decay from 0.88178, and it strictly improves the named published Fiori--Kadiri--Swidinsky constants.

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