Shikao Ikehara

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Shikao Ikehara (池原 止戈夫 Ikehara Shikao; 1904 – 1984) is a Japanese mathematician. He was a student of Norbert Wiener at MIT (PhD 1930). Ikehara, using Wiener's Tauberian theory, established his famous Tauberian theorem, and derived a new proof of the prime number theorem. In particular he showed that the prime number theorem is equivalent to the non-vanishing of the zeta function on the line Re s = 1. Earlier proofs of the prime number theorem relied on the just mentionned non-vanishing property of the zeta function, together with some bounds on the order of growth of the zeta function (see Landau's book).

[edit] See also

• Wiener-Ikehara theorem