Meromorphic Continuation of the Goldbach Generating Function
نویسنده
چکیده
To shift the path of integration to the left, one needs at least meromorphic continuation to some half-plane R s > r− δ as well as some information on the growth and the distribution of the poles of Φr. Assuming the Riemann hypothesis, Egami and Matsumoto[4] described the behavior for the case r = 2. In addition to the RH, parts of their results depend on unproved assumptions on the distribution of the imaginary parts of zeros of ζ. Denote by Γ the set of imaginary parts of non-trivial zeros of ζ. While the assumption that the positive elements in Γ are rationally independent appears to be folklore, Fujii[5] drew attention to the following special case:
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