On the sum and the regularized products of some Dirichlet series

On the sum and the regularized products of some Dirichlet series

In this paper, using zeta functions, we evaluate the regularized products of some Dirichlet series generalizing Lerch’s formula and we show that they are multiplicative. As an application, we determine the sum of some Dirichlet series generalizing Euler’s formula on the sum of the reciprocal of squa...

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Veröffentlicht in:The Ramanujan journal 2024-12, Vol.65 (4), p.1799-1812
1. Verfasser: Hajli, Mounir
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Series (mathematics)
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Beschreibung
Zusammenfassung:In this paper, using zeta functions, we evaluate the regularized products of some Dirichlet series generalizing Lerch’s formula and we show that they are multiplicative. As an application, we determine the sum of some Dirichlet series generalizing Euler’s formula on the sum of the reciprocal of squares.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-023-00796-0