Structural properties of Dirichlet series with harmonic coefficients

An infinite family of functional equations in the complex plane is obtained for Dirichlet series involving harmonic numbers. Trigonometric series whose coefficients are linear forms with rational coefficients in hyperharmonic numbers up to any order are evaluated via Bernoulli polynomials, Gauss sum...

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Veröffentlicht in:	The Ramanujan journal Jg. 45; H. 2; S. 569 - 600
Hauptverfasser:	Alkan, Emre, Göral, Haydar
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.02.2018 Springer Nature B.V
Schlagworte:	Coefficients Combinatorics Dirichlet problem Field Theory and Polynomials Fourier Analysis Functional equations Functions (mathematics) Functions of a Complex Variable Mathematical analysis Mathematics Mathematics and Statistics Number Theory Real numbers Representations Polylogarithm 11M41 Harmonic number 30B50 Functional equation 33B10 30D05 Dirichlet series Gauss sum Catalan’s constant
ISSN:	1382-4090, 1572-9303
Online-Zugang:	Volltext
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