Dirichlet Series

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Dirichlet series [‚dē·rē′klā ‚sir·ēz]

(mathematics)

A series whosenth term is a complex number divided bynto thezth power.

Dirichlet Series

(named for P. G. L. Dirichlet), series of the form

where the a_n are constants and s = σ + it is a complex variable. For example, the series

represents the zeta function for σ > 1. The theory of Dirichlet series originally arose under the strong influence of analytic number theory. Eventually it developed into an extensive branch in the theory of analytic functions.

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No references found			6) 2 Some proofs by Hamburger The proofs by Hamburger just mentioned are given by him for functions defined by Dirichlet series, but specialisation to the present case is an easy matter. The Riemann Zeta function and the sampling theorem by Higgins, J.R. / Sampling Theory in Signal and Image Processing Introduction Harald Bohr's interest in which functions could be represented by a Dirichlet series, i. Almost periodic functions with values in p-frechet spaces, 0 < p < 1 by Gal, Sorin G.; N'Guerekata, Gaston M. / Global Journal of Pure and Applied Mathematics For r > 0, the Dirichlet series involved are convergent. Lattice reduction in two dimensions: analyses under realistic ... by Vallee, Brigitte; Vera, Antonio / DMTCS Proceedings			directories Directory Directory Access Protocol directory board directory harvest attack directory listings directory management directory path directory server directory service Directory System Agent directory tree Directory User Agent Directory, Ukrainian Directrix DirectSound DirectX DirectX 10 dirge Dirham Dirichlet conditions Dirichlet drawer principle Dirichlet Integral Dirichlet Principle Dirichlet Problem Dirichlet Series Dirichlet test for convergence Dirichlet theorem Dirichlet transform Dirichlet, Peter Gustav Lejeune Dirigible Dirk Dirk Jan Struik Dirk Volkertszoon Coornhert Dirksen, Everett Dirksen, Everett McKinley Dirr, Adolf Dirschau dirt dirt band dirt bed dirt chimney dirt resistance dirt slip dirt-and-stick chimney dirt-depreciation factor dirtball Dirtiness dirty dirty bit dirty bomb			Dirges Dirges Dirges dirgha Dirgible Dirgible dIRH dirham dirham dirham dirhams dirhams dirhams Dirhem Dirhem Diri Diricawl Diricawl Dirichlet Dirichlet box principle Dirichlet character Dirichlet conditions Dirichlet domain Dirichlet drawer principle Dirichlet Free-Form Deformation Dirichlet integral Dirichlet Integrals Dirichlet principle Dirichlet problem Dirichlet Problems Dirichlet Series Dirichlet tesselation Dirichlet tessellation Dirichlet test for convergence Dirichlet theorem Dirichlet transform Dirichlet's Box Principle Dirichlet's conditions Dirichlet's drawer principle Dirichlet's principle Dirichlet's problem Dirichlet's theorem on arithmetic progressions Dirichlet, Peter Gustav Lejeune Dirichlet-Biomial Attribute Test DIRID Dirige Dirige Dirigeant-Entrepreneur du Secteur des Métiers Dirigeants Commerciaux de France Dirigeants Commerciaux Francophones en Hongrie Dirigeants de la Formation Professionnelle Dirigeants-Durables Midi-Pyrénées Dirigent dirigere dirigere dirigible dirigible Dirigibles Dirigibles

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