Abstract
Theorem A. Let q ≥ O and r ≥ O be integers. Let s = σ + it, let ζ(s) be the Riemann zeta-function, let Go(s) = 1, and [Formula: see text] and let F(s) = Gq(s)/Hr(s). Then as t → ∞ lim sup [unk]F(1 + it)[unk]/(log log t)q+r+1 ≥ (6/π)2)r+1 exp {(q + r + 1)γ}, where γ is Euler's constant.
Stronger results such as proved in [1] are valid, and in particular q and r can be allowed to increase with t as in [1]. Results involving the real part of the sum of the factors of Gq and of the reciprocals of the factors of Hr can be proved much as in [3].
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Selected References
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