Abstract
AbstractWe show how the classical polylogarithm function $$\textrm{Li}_s(z)$$
Li
s
(
z
)
and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution $$(x+i 0)^s$$
(
x
+
i
0
)
s
. We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemann’s zeta function, Master of Science, Ohio State University, Mathematics (1975)].
Publisher
Springer Science and Business Media LLC
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