Correction to: “Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem” [J. Number Theory 130 (2010) 707–715]

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We discuss the main result of [1] which is concerned with the study of generalised prime systems for which the integer counting function NP(x) is asymptotically very well-behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and β<12. For such systems, the associated zeta function ζP(s) is holomorphic for σ=ℜs>β. It was claimed that for β<σ<12, ∫0T|ζP(σ+it)|2dt=Ω(T2−2σ−ε) for (i) any ε>0, and (ii) for ε=0 for all such σ except possibly one value.The proof of these statements contains a flaw however, and in this Corrigendum we indicate where the mistake occurred but show that the proof can be rectified to still obtain (i) and get a slightly weaker result for (ii). The resulting Corollary 2 of [1] concerning the Dirichlet divisor problem for generalised integers remains essentially correct.