id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6387	amen, zhwan; Al-Maamori, Faez; Fattah Hama, mudhafar	The Effect of Variation in the Order of the Beurling Zeta Function in the Strip (0, 1) on the Upper Bound of Nₚ(x)	2025	15	.pdf	application/pdf	5528	327	83	= li(x) +O(xe−k √ log x) for some k > 0, where li(x) = ∫ x 2 dt log t (iii) In 2006, Diamond, Montogomery and Vorhauer [18] showed that Landau’s result is best possiblre. So, we get exp [( 1 + t100(1−σ) 3 2 ) (log t) 2 3 ] ≤ t 1 2( 1 + t100(1−σ) 3 2 ) (log t) 2 3 ≤ log t 1 2( 1 + e100(1−σ) 3 2 log t ) ≤ 1 2 (log t) 1 3 e100(1−σ) 3 2 log t ≤ 1 + e100(1−σ) 3 2 log t ≤ 1 2 (log t) 1 3 so e100(1−σ) 3 2 log t ≤ 1 2 (log t) 1 3 log ( e100(1−σ) 3 2 log t ) ≤ log ( 1 2 (log t) 1 3 ) 100(1− σ) 3 2 log t ≤ log( 1 2 ) + log ( (log t) 1 3 ) (1− σ) 3 2 ≤ log 1 2 + 1 3 log log t 100 log t log ( e100(1−σ) 3 2 log t ) ≤ log ( 1 2 (log t) 1 3 ) 100(1− σ) 3 2 log t ≤ log( 1 2 ) + log ( (log t) 1 3 ) (1− σ) 3 2 ≤ log 1 2 + 1 3 log log t 100 log t Z. M. Amen, F. A. Al-Maamori, M. F. Hama / Eur.	cache/ejpam-6387.pdf	txt/ejpam-6387.txt