Norman Levinson

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

Life and work

Levinson was the son of poor Jewish immigrants from Russia. In 1929 he began to study electrical engineering at MIT. In 1934 he received his degree. Besides, he had already occupied almost all mathematics courses offered and discovered in 1933 during a visit to a course on Fourier analysis with Norbert Wiener, a gap in a working and closed, the Viennese had given him for proofreading. It was his first (of Viennese personally typed and be sent ) mathematical publication. After that he went on a scholarship to Cambridge to Hardy and Littlewood. In 1935, he received his doctorate at MIT and then went to John von Neumann to the Institute for Advanced Study. In 1937 he was instructor at MIT (on special recommendation of Wiener and Hardy, the director Vannevar Bush wanted to not hire Jews ) and 1939 assistant professor ( he received a full professorship in 1949 ). In 1940 he completed his studies for Fourier Analysis from with his book, Gap and density theorems (AMS Colloquium Publication Series ) and turned to the theory of nonlinear differential equations, where it is partially built on the work of Littlewood and Cartwright. His work in this field he summarized in the book Theory of Ordinary Differential Equations of 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- Khinchin theorem for discrete-time signals) had direct practical applications in geophysics (eg in the offshore oil exploration ). In 1971 he received the Chauvenet Prize. In the 1970s, he turned to the analytic number theory and proved that at least one third of the non-trivial zeros of the Riemann zeta function on the critical line (real part 1/2) are an important step in the history of proof attempts to still open Riemann Hypothesis. Shortly thereafter, he was diagnosed with a brain tumor and died.

Levinson had been married since 1938 and had two daughters.

In 1971 he received the Chauvenet Prize for A Motivated Account of an Elementary Proof of the Prime Number Theorem.

Among its 34 doctoral counts Raymond Redheffer.

Writings

• John A. Nohel, David H. Sattinger (Editor ): Selected papers of Norman Levinson, MIT, Birkhäuser, 1998
• With Earl Coddington: Theory of ordinary differential equations, McGraw Hill 1972, Warrior 1984
• Gap and density theorems, AMS Colloquium Publications 1940
• More than one third of zeros of Riemann's zeta function are on Advances in Mathematics, Bd.13, 1974, p 383-436