Shikao Ikehara
From Wikipedia, the free encyclopedia
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). Ikehara, using Wiener's Tauberian theory, established the Wiener-Ikehara 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 mentioned non-vanishing property of the zeta function, together with some bounds on the order of growth of the zeta function.
[edit] 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.
