Abstract
constant factor) if it satisfies Riemann's functional equation. This result was placed in an altogether more general setting by Hecke's work [9] on the correspondence between Dirichlet series with given signature (introduced by him), and modular functions. This paper is also concerned with that problem, but from a different approach. Hamburger's theorem [16, p. 31] states that if G(s) is an entire function of finite order, P(s) a polynomial, and f(s) = G(s)/P(s), and
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