Norman Levinson

Norman Levinson (born August 11, 1912 in Lynn , Massachusetts , † October 10, 1975 in Boston ) was an American mathematician who worked in the field of analysis ( harmonic analysis , differential equations ) and analytical number theory .

life and work

Levinson was the son of poor Jewish emigrants from Russia. In 1929 he began to study electrical engineering at MIT . In 1934 he graduated. In addition, he had already taken almost all of the mathematics courses on offer and in 1933, while attending a course on Fourier analysis with Norbert Wiener, discovered and closed a gap in a thesis that Wiener had given him to proofread. This resulted in his first mathematical publication (typed and sent in personally by Wiener). Then he went to Cambridge on a scholarship to Hardy and Littlewood . In 1935 he received his doctorate from MIT and then went to John von Neumann at the Institute for Advanced Study . In 1937 he became an instructor at MIT (on the special recommendation of Wiener and Hardy, the director Vannevar Bush actually did not want to employ Jews) and in 1939 an assistant professor (he did not receive a full professorship until 1949). In 1940 he completed his studies on Fourier analysis with his book Gap and density theorems (AMS Colloquium Publication Series) and turned to the theory of nonlinear differential equations, building in part on the work of Littlewood and Cartwright. He summarized his work in this area in the book Theory of Ordinary Differential Equations from 1955 (with Earl Coddington). In 1953 he received the Bôcher Memorial Prize for this work . Levinson also worked on inverse problems . His work on time series (he formulated the Wiener-Chintschin theorem for discrete-time signals) had direct practical applications in geophysics (e.g. in offshore oil exploration). In the 1970s he turned to analytical number theory and proved that at least one third of the non-trivial zeros of the Riemann zeta function lie on the critical line (real part 1/2), an important step in the history of attempts to prove the still open Riemann Hypothesis . Shortly afterwards, he developed a brain tumor and died.

Levinson had been married since 1938 and had two daughters.

In 1945 Levinson was elected to the American Academy of Arts and Sciences , in 1967 to the National Academy of Sciences . In 1971 he received the Chauvenet Prize for A Motivated Account of an Elementary Proof of the Prime Number Theorem .

Raymond Redheffer is one of his 34 PhD students .

Fonts

• John A. Nohel, David H. Sattinger (editors): Selected papers of Norman Levinson , MIT, Birkhäuser, 1998
• with Earl Coddington: Theory of ordinary differential equations , McGraw Hill 1972, Krieger 1984
• Gap and density theorems , AMS Colloquium Publications 1940
• More than one third of Zeros of Riemann's Zeta Function are on ${\displaystyle \sigma ={\frac {1}{2}}}$ , Advances in Mathematics, Vol. 13, 1974, pp. 383-436

Web links

• John J. O'Connor, Edmund F. Robertson :  Norman Levinson. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Levinson, American Mathematical Monthly, Vol. 76, 1969, pp. 225-245