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On the order of growth of Lerch zeta functions
Please always quote using this URN: urn:nbn:de:bvb:20-opus-303981
- We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t\(^{13/84+ϵ}\) as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t\(^ϵ\) (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.
Author: | Jörn Steuding, Janyarak Tongsomporn |
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URN: | urn:nbn:de:bvb:20-opus-303981 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Mathematics |
ISSN: | 2227-7390 |
Year of Completion: | 2023 |
Volume: | 11 |
Issue: | 3 |
Article Number: | 723 |
Source: | Mathematics (2023) 11:3, 723. https://doi.org/10.3390/math11030723 |
DOI: | https://doi.org/10.3390/math11030723 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | (approximate) functional equation; Hurwitz zeta function; Lerch zeta function; MSC 11M35; exponent pairs; order of growth |
Release Date: | 2024/03/06 |
Date of first Publication: | 2023/02/01 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |