Winner of the Fields medal in 1950, Selberg contributed major ideas to analysis and number theory.
His most important contribution is the Selberg Trace Formula, a fundamental tool in harmonic analysis on Lie Groups, which is especially useful in the study of automorphic forms.
The Fields medal was awarded to Selberg for his elementary proof of the Prime Number Theorem. He also invented the Selberg Sieve and developed the general theory of sieves. He made many contributions to the theory of the Riemann zeta-function. He was the first to prove that the Riemann zeta-function has a positive proportion of its zeros on the critical line and laid the groundwork for the proof that the logarithm of the Riemann zeta-function is normally distributed on the critical line. And the Rankin-Selberg convolution, a method for creating new L-functions out of old, opened the door to a grander theory of L-functions.
In 1944 in a Norwegian College Teachers journal, Selberg published a paper on what is now called Selberg's Integral, a fundamental identity in random matrix theory.
Selberg also proved his rigidity theorem, that lattices in Lie groups of rank larger than two cannot be continuously deformed.
Selberg was part of the permanent faculty at the Institute for Advanced Study, having joined that faculty in 1949.
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