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On Schlömilch series associated¶with certain Dirichlet series |
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| Authors: | Ettore Carletti Giacomo Monti Bragadin |
| Affiliation: | Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35,?I-16146 Genova, Italy. e-mail: carletti@dima.unige.it, IT Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, I-16146 Genova, Italy. e-mail: monti@dima.unige.it, IT |
| Abstract: | In this paper we prove that the Dirichlet series , where a(n) is a quasi-polynomial and a, b are distinct non negative rational numbers, is, in a left half plane, a finite sum of Schl?milch-type series. As a worthwhile application we get the value at positive integers of the Hurwitz double zeta-function , , , as well as some information on L(s;a)' real zeros. Received: 20 October 1997 / Revised version: 23 April 1998 |
| Keywords: | Mathematics Subject Classification (1991):Primary 11M41 |
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