# Mathematician:Norman Levinson

## Mathematician

American mathematician whose major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.

Worked closely with Norbert Wiener in his early career.

In $1974$ he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.

American

## History

• Born: 11 August 1912 in Lynn, Massachusetts, USA
• 1929: Entered the Massachusetts Institute of Technology to study electrical engineering
• 1934: Awarded a Bachelor of Science degree and a Master of Science degree, both in electrical engineering
• 1937: Joined the faculty of the Massachusetts Institute of Technology
• 1944: Promoted to Associate Professor in 1944
• 1949: Promoted to full Professor
• 1954: Awarded the Bôcher Memorial Prize of the American Mathematical Society
• 1970: Awarded the Lester R. Ford Award
• 1971: Awarded the Chauvenet Prize
• Died: 10 October 1975 in Boston, Massachusetts, USA of a brain tumour

## Publications

• 1935: On the Non-Vanishing of a Function (D.Sc. Thesis)
• 1940: Gap and Density Theorems
• 1947: The Wiener RMS error criterion in filter design and prediction (J. Math. Phys. Vol. 25: 261 – 278)
• 1955: Theory of ordinary differential equations (with Earl A. Coddington)
• 1964: Generalization of an inequality of Ky Fan (J. Math. Anal. Appl. Vol. 8: 133 – 134)
• 1968: Summing certain number theoretic series arising in the sieve (J. Math. Anal. Appl. Vol. 22: 631 – 645)
• 1969: A Motivated Account of an Elementary Proof of the Prime Number Theorem (Amer. Math. Monthly Vol. 76: 225 – 245)
• February 1973: Remarks on a formula of Riemann for his zeta-function (J. Math. Anal. Appl. Vol. 41no. 2: 345 – 351)
• 1974: Zeros of the Derivatives of the Riemann Zeta Function (Acta Math. Vol. 133: 49 – 65) (with Hugh Lowell Montgomery)
• April 1974: At least one third of the zeros of Riemann's zeta-function are on $\sigma = 1/2$ (Proc. Natl. Acad. Sci. U S A Vol. 71: 1013 – 1015)  www.jstor.org/stable/63251
• August 1974: More than one third of zeros of Riemann's zeta-function are on $\sigma = 1/2$ (Advances in Mathematics Vol. 13no. 4: 383 – 436)

## Critical View

One day shortly after his paper on the Riemann zeta function appeared, he knocked at the door, came in, and sat down. He looked pale and ill. He complained of a strong headache. ... Shortly afterwards, he entered Massachusetts General Hospital. ... in the August of that summer [I] visited him ... His head was shaven, and red and black lines were drawn on it. ... I never saw him again.
-- Gian-Carlo Rota