# Mathematician:Norman Levinson

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## 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.

## Nationality

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

## Theorems and Definitions

## 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**: pp. 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**: pp. 133 – 134) - 1968:
*Summing certain number theoretic series arising in the sieve*(*J. Math. Anal. Appl.***Vol. 22**: pp. 631 – 645) - 1969:
*A Motivated Account of an Elementary Proof of the Prime Number Theorem*(*Amer. Math. Monthly***Vol. 76**: pp. 225 – 245) - February 1973:
*Remarks on a formula of Riemann for his zeta-function*(*J. Math. Anal. Appl.***Vol. 41**,*no. 2*: pp. 345 – 351) - 1974:
*Zeros of the Derivatives of the Riemann Zeta Function*(*Acta Math.***Vol. 133**: pp. 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**: pp. 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. 13**,*no. 4*: pp. 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.*