Shikao Ikehara

Shikao Ikehara (池原 止戈夫, Ikehara Shikao, April 11, 1904 – October 10, 1984) was a Japanese mathematician. He was a student of Norbert Wiener at MIT (PhD 1930). After Wiener in 1928, and by using Wiener's Tauberian theory, Ikehara derived in 1931 another proof of the prime number theorem only using the non-vanishing of the zeta function on the line Re s = 1. Proofs of the prime number theorem before 1928 and only using the behaviour of the zeta function on the line Re s = 1 (as the 1908 proof of Edmund Landau), also appealed to some bound on the order of growth of the zeta function on this line. An improved version of Ikehara's 1931 result by Wiener in 1932 is now known as the Wiener-Ikehara theorem. Returning to Japan after studying with Dr Wiener, he taught at Osaka University^[1] and the Tokyo Institute of Technology, and translated Cybernetics: Or Control and Communication in the Animal and Machine into Japanese.^[2]

References

• S. Ikehara (1931). "An extension of Landau's theorem in the analytic theory of numbers". Journal of Mathematics and Physics of the Massachusetts Institute of Technology. 10: 1–12. Zbl 0001.12902. 
• Shikao Ikehara at the Mathematics Genealogy Project