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Ewald expansions of a class of zeta-functions
| Content Provider | Paperity |
|---|---|
| Author | Tsukada, Haruo Chakraborty, Kalyan Kanemitsu, Shigeru |
| Abstract | The incomplete gamma function expansion for the perturbed Epstein zeta function is known as Ewald expansion. In this paper we state a special case of the main formula in Kanemitsu and Tsukada (Contributions to the theory of zeta-functions: the modular relation supremacy. World Scientific, Singapore, 2014) whose specifications will give Ewald expansions in the H-function hierarchy. An Ewald expansion for us are given by \(H_{1,2}^{2,0}\leftrightarrow H_{1,2}^{1,1}\) or its variants. We shall treat the case of zeta functions which satisfy functional equation with a single gamma factor which includes both the Riemann as well as the Hecke type of functional equations and unify them in Theorem 2. This result reveals the H-function hierarchy: the confluent hypergeometric function series entailing the Ewald expansions. Further we show that some special cases of this theorem entails various well known results, e.g., Bochner–Chandrasekharan theorem, Atkinson–Berndt theorem etc. |
| Starting Page | 99 |
| File Format | HTM / HTML |
| DOI | 10.1186/s40064-016-1732-5 |
| Issue Number | 1 |
| Journal | SpringerPlus |
| Volume Number | 5 |
| e-ISSN | 21931801 |
| Language | English |
| Publisher | Springer International Publishing |
| Publisher Date | 2016-02-01 |
| Access Restriction | Open |
| Subject Keyword | Primary 11r42 secondary 11r11 Modular relation Ewald expansion Zeta-function Functional equation |
| Content Type | Text |
| Resource Type | Article |
