was a Japanese mathematician. He was a student of

Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...

at MIT (

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

1930). Following Wiener in 1928, in 1931 Ikehara used Wiener's Tauberian theory to derive another proof of the

prime number theorem In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying ...

, demonstrated solely via the non-vanishing of the zeta function on the line Re s = 1. An improved version of Ikehara's 1931 result by Wiener in 1932 is now known as the

Wiener–Ikehara theorem The Wiener–Ikehara theorem is a Tauberian theorem introduced by . It follows from Wiener's Tauberian theorem, and can be used to prove the prime number theorem (Chandrasekharan, 1969). Statement Let ''A''(''x'') be a non-negative, monotonic no ...

. 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. Returning to Japan after studying with Dr Wiener, he taught at

Osaka University , abbreviated as , is a public research university located in Osaka Prefecture, Japan. It is one of Japan's former Imperial Universities and a Designated National University listed as a "Top Type" university in the Top Global University Project. ...

and the Tokyo Institute of Technology. He translated '' Cybernetics: Or Control and Communication in the Animal and Machine'' into Japanese.Wiener, N. (1956). 'Preface to the Japanese Translation of Cybernetics.' anuscriptMIT Special Collections Archive, MC22. Cambridge.

References

* * {{DEFAULTSORT:Ikehara Shikao 1904 births 1984 deaths 20th-century Japanese mathematicians