Modified L-functions
The sequence of generalized prime numbers q0 = 1, qn = pkn+1 -1, n ∈ N, and the corresponding zeta-function Zk(s) = \prodp>2( 1 - (pk - 1)-s)-1 , s = σ + it, are analyzed. The analyticity of Zk(s) in the domain σ > 0, except for a simple pole s = 1/k , is proved.
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2008-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/18059 |
| _version_ | 1818336156419358720 |
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| author | Eugenijus Stankus |
| author_facet | Eugenijus Stankus |
| author_sort | Eugenijus Stankus |
| collection | DOAJ |
| description | The sequence of generalized prime numbers q0 = 1, qn = pkn+1 -1, n ∈ N, and the corresponding zeta-function Zk(s) = \prodp>2( 1 - (pk - 1)-s)-1 , s = σ + it, are analyzed. The analyticity of Zk(s) in the domain σ > 0, except for a simple pole s = 1/k , is proved. |
| first_indexed | 2024-12-13T14:34:50Z |
| format | Article |
| id | doaj.art-26cc5d4ef85e494aa5a40375d9025c1a |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-12-13T14:34:50Z |
| publishDate | 2008-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-26cc5d4ef85e494aa5a40375d9025c1a2022-12-21T23:41:44ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2008-12-0148proc. LMS10.15388/LMR.2008.07Modified L-functionsEugenijus Stankus0Vilnius UniversityThe sequence of generalized prime numbers q0 = 1, qn = pkn+1 -1, n ∈ N, and the corresponding zeta-function Zk(s) = \prodp>2( 1 - (pk - 1)-s)-1 , s = σ + it, are analyzed. The analyticity of Zk(s) in the domain σ > 0, except for a simple pole s = 1/k , is proved.https://www.journals.vu.lt/LMR/article/view/18059analyticitygeneralized numberL-functionresiduezeta-function |
| spellingShingle | Eugenijus Stankus Modified L-functions Lietuvos Matematikos Rinkinys analyticity generalized number L-function residue zeta-function |
| title | Modified L-functions |
| title_full | Modified L-functions |
| title_fullStr | Modified L-functions |
| title_full_unstemmed | Modified L-functions |
| title_short | Modified L-functions |
| title_sort | modified l functions |
| topic | analyticity generalized number L-function residue zeta-function |
| url | https://www.journals.vu.lt/LMR/article/view/18059 |
| work_keys_str_mv | AT eugenijusstankus modifiedlfunctions |