Around the Lipschitz Summation Formula

Wenbin Li, Hongyu Li and Jay Mehta

Mathematical Problems in Engineering, 2020, vol. 2020, 1-16

Abstract:

Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa-Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula. Our purpose is to show that it is a form of the functional equation for the Lipschitz–Lerch transcendent (and in the long run, it is equivalent to that for the Riemann zeta-function) and that this being indeed a boundary function of the Hurwitz–Lerch zeta-function, one can extract essential information. We also elucidate the relation between Ramanujan’s formula and automorphy of Eisenstein series.

Date: 2020
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2020/5762823.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2020/5762823.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:5762823

DOI: 10.1155/2020/5762823

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().