1. Non-real poles and irregularity of distribution.
- Author
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Lowry-Duda, David
- Subjects
- *
PRIME number theorem , *DIRICHLET series , *POLISH people , *TAUBERIAN theorems - 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. We include several applications. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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