Abstract
Assuming the simplicity of the zeros of the Riemann zeta function [Formula: see text], Gonek and Hejhal studied the sum [Formula: see text] for real number [Formula: see text] and conjectured that [Formula: see text] for any real [Formula: see text]. Assuming Riemann hypothesis and [Formula: see text], Ng [11] proved that the Mertens function [Formula: see text]. He also pointed out that with the additional hypothesis of [Formula: see text] one gets [Formula: see text]. Here we show that [Formula: see text] for any real number [Formula: see text], under similar hypotheses.
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