An Additional Writing on Lagarias–suzuki (2006)

نویسندگان

  • MASATOSHI SUZUKI
  • M. SUZUKI
چکیده

At first, we show the following matter. Theorem 1. Let H∗(y; s) be as above. Suppose that y ≥ 1 and p(s) has N many zeros counted with multiplicity in the right half-plane R(s) > 1/2. Then H∗(y; s) has at most N +1 many zeros in the right half-plane R(s) > 1/2 counting with multiplicity, and the same thing holds in the left half-plane R(s) < 1/2. The trivial functional equation H(y; s) = H(y; 1− s) implies H∗(y; 1− s) = −H∗(y; s). Therefore, it suffices to study the zeros of H∗(y; s) in the right half-plane R(s) > 1/2. In what follows, we suppose that σ = R(s) > 1/2.

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تاریخ انتشار 2014