Functional equation of a special Dirichlet series
In this paper we study the special Dirichlet series L(s)=23∑n=1∞sin(2πn3)n−s, s∈C This series converges uniformly in the half-plane Re(s)>1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The valu...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000462 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper we study the special Dirichlet series
L(s)=23∑n=1∞sin(2πn3)n−s, s∈C
This series converges uniformly in the half-plane Re(s)>1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The values of the function L at the points 0,±1,−2,±3,−4,±5,… are obtained. The values at the positive integers 1,3,5,… are determined by means of a functional equation satisfied by L. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |