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Non-real poles and irregularity of distribution.
- Source :
-
Journal of Number Theory . Dec2020, Vol. 217, p23-35. 13p. - Publication Year :
- 2020
-
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]
- Subjects :
- *PRIME number theorem
*DIRICHLET series
*POLISH people
*TAUBERIAN theorems
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 217
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 145415254
- Full Text :
- https://doi.org/10.1016/j.jnt.2020.05.007