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arXiv · 0912.2390

On certain sums over the nontrivial zeta zeros

Mark W. Coffey
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Abstract

We study coefficients $b_n$ that are expressible as sums over the Li/Keiper constants $λ_j$. We present a number of relations for and representations of $b_n$. These include the expression of $b_n$ as a sum over nontrivial zeros of the Riemann zeta function, as well as integral representations. Conditional on the Riemann hypothesis, we provide the asymptotic form of $b_n \sim 2^{-n-2}\ln n$.

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Mark W. Coffey. 2009-12-12. On certain sums over the nontrivial zeta zeros. https://doi.org/10.1098/rspa.2010.0064

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