ABSTRACT. Said Sn(s) the nth partial sum of the Dirichlet η function, and Rn(s) the corresponding remainder term, by combining an analytic approach with a geometric one it is shown that inside the critical strip, for any pair of critical line symmetrical arguments, ρ = 1 2 + α + it and τ = 1 2 − α + it, the inequality limn→ ∞ |Sn(ρ)|/|Sn(τ) |> limn→ ∞ |Rn(ρ)|/|Rn(τ) | always holds. However, making the additional hypothesis that said pair of critical line symmetrical arguments corresponds to a pair of zeros would instead result in limn→ ∞ |Sn(ρ)|/|Sn(τ) | = limn→ ∞ |Rn(ρ)|/|Rn(τ) | = 0. This contradicting result suggests that in the interior of the critical strip there cannot be zeros of η lying off the critical line. 1
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