A local Riemann hypothesis, I

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The Riemann hypothesis for certain integrals of Eisenstein series (解析的整数論とその周辺研究集会報告集) (2004, background): “Bump’s point in [ 5 ] is to make an analogy with metaplectic Eisenstein series, see the discussion in §5.) The observation follows because the finite Dirichlet series �s(n) is easily shown from its Euler product to have all zeros on the imaginary axis ℜ(s) = 0. In addition, for fixed y > 0 the K-Bes”
ZEROS OF CERTAIN POLYNOMIALS (2016, background): “3) Our original motivation to study the roots of Hilbert polynomials arose from reading [ BChKV ].”
Ehrhart polynomials and successive minima (2005, background): “It follows from a much more general result of Bump et al. [ 12, Theorem 4 ] that the zeros of G(s, C ∗ n ) all have real parts equal to −1/2.”