Generalised Dirichlet series and Hecke's functional equation
1967 ◽
Vol 15
(4)
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pp. 309-313
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Keyword(s):
The generalised zeta-function ζ(s, α) is defined bywhere α>0 and Res>l. Clearly, ζ(s, 1)=, where ζ(s) denotes the Riemann zeta-function. In this paper we consider a general class of Dirichlet series satisfying a functional equation similar to that of ζ(s). If ø(s) is such a series, we analogously define ø(s, α). We shall derive a representation for ø(s, α) which will be valid in the entire complex s-plane. From this representation we determine some simple properties of ø(s, α).
1932 ◽
Vol 28
(3)
◽
pp. 273-274
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Keyword(s):
Keyword(s):
1984 ◽
Vol 19
(1)
◽
pp. 85-102
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Keyword(s):
2018 ◽
Vol 14
(02)
◽
pp. 371-382
2013 ◽
Vol 97
(540)
◽
pp. 455-460
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Keyword(s):