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arXiv · 1910.09969

Non-real Poles and Irregularity of Distribution

David Lowry-Duda
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Abstract

We study the general theory of weighted Dirichlet series and associated summatory functions of their coefficients. We show that any non-real pole leads to oscillatory error terms. This applies even if there are infinitely many non-real poles with the same real part. Further, we consider the case when the non-real poles lie near, but not on, a line. The method of proof is a generalization of classical ideas applied to study the oscillatory behavior of the error term in the prime number theorem.

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David Lowry-Duda. 2019-10-22. Non-real Poles and Irregularity of Distribution. https://doi.org/10.1016/j.jnt.2020.05.007

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