Geodesic
An identity for certain Dirichlet series†
Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 79-82

Voir la notice de l'article provenant de la source Cambridge University Press

In deriving the approximate functional equation for certain Dirichlet series, one first establishes an identity for the function in terms of a partial sum of the series (e.g. see [1] and [2]). It is the purpose of this note to give a short proof of this identity for Hecke's Dirichlet series [1]. The proof is valid with only a few minor changes for the identity given by Chandrasekharan and Narasimhan [2, Lemma 2] for a much larger class of Dirichlet series. However, the brevity of the paper would be lost if we introduced the necessary terminology and notation. 
Berndt, B. C. An identity for certain Dirichlet series†. Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 79-82. doi: 10.1017/S001708950000032X
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[1] 1.Apostol, T. M. and Sklar, Abe, The approximate functional equation of Hecke's Dirichlet series, Trans. Amer. Math. Soc. 86 (1957), 446–462. Google Scholar

[2] 2.Chandrasekharan, K. and Narasimhan, Raghavan, The approximate functional equation for a class of zeta-functions, Math. Ann. 152 (1963), 30–64. Google Scholar | DOI

[3] 3.Hobson, E. W., The theory of functions of a real variable, vol. II, 2nd. ed., Cambridge University Press (Cambridge, 1926). Google Scholar

[4] 4.Titchmarsh, E. C., Theory of Fourier integrals, 2nd. ed., Clarendon Press (Oxford, 1948). Google Scholar

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