Abstract
Hamburger's theorem, which characterizes the Riemann zeta function by means of its functional equation, has tempted a number of researchers to find an alternative proof and/or a generalization. A characterization of hyper-functions has been proved on Rn whose supports, as well as the supports of their Fourier transforms, are contained in Zn. Claiming the existence of functional equations of a certain family of L-functions with Größencharacters, a formula is derieved similar to the Poisson summation formula. The chapter explains the method of Ehrenpreis, Kawai, and Yoshimoto to prove the Hamburger theorem for the Epstein zeta function, a typical example of zeta functions associated with prehomogeneous vector spaces.
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