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Around the Lipschitz Summation Formula
Joint Authors
Li, Wenbin
Li, Hongyu
Mehta, Jay
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-23
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Li, Wenbin& Li, Hongyu& Mehta, Jay. 2020. Around the Lipschitz Summation Formula. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1196247
Modern Language Association (MLA)
Li, Wenbin…[et al.]. Around the Lipschitz Summation Formula. Mathematical Problems in Engineering No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1196247
American Medical Association (AMA)
Li, Wenbin& Li, Hongyu& Mehta, Jay. Around the Lipschitz Summation Formula. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1196247
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1196247