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On the values of a class of Dirichlet series at rational arguments
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| Zeitschriftentitel: | Proceedings of the American Mathematical Society |
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| Personen und Körperschaften: | , , |
| In: | Proceedings of the American Mathematical Society, 138, 2009, 4, S. 1223-1230 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
American Mathematical Society (AMS)
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| Schlagwörter: |
| Zusammenfassung: | <p>In this paper we shall prove that the combination of the general distribution property and the functional equation for the Lipschitz-Lerch transcendent capture the whole spectrum of deeper results on the relations between the values at rational arguments of functions of a class of zeta-functions. By Theorem 1 and its corollaries, we can cover all the previous results in a rather simple and lucid way. By considering the limiting cases, we can also deduce new striking identities for Milnor’s gamma functions, among which is the Gauss second formula for the digamma function.</p> |
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| Umfang: | 1223-1230 |
| ISSN: |
0002-9939
1088-6826 |
| DOI: | 10.1090/s0002-9939-09-10171-5 |