World War II
During World War II, Selberg worked in isolation due to the German occupation of Norway. After the war his accomplishments became known, including a proof that a positive proportion of the zeros of the Riemann zeta function lie on the line .
After the war, he turned to sieve theory, a previously neglected topic which Selberg's work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a method well adapted in particular to providing auxiliary upper bounds, and which contributed to Chen's theorem, among other important results.
In March 1948, Selberg established, by elementary means, the asymptotic formula
where
for primes . By July of that year, Selberg and Paul Erdős had each obtained elementary proofs of the prime number theorem, both using Selberg's then unpublished asymptotic formula as a starting point. Circumstances leading up to the proofs, as well as publication disagreements, led to a bitter dispute between the two mathematicians.
For his fundamental accomplishments during the 1940s, Selberg received the 1950 Fields Medal.
Read more about this topic: Atle Selberg
Famous quotes containing the words world war, world and/or war:
“One ... aspect of the case for World War II is that while it was still a shooting affair it taught us survivors a great deal about daily living which is valuable to us now that it is, ethically at least, a question of cold weapons and hot words.”
—M.F.K. Fisher (1908–1992)
“At the heart of all beauty lies something inhuman, and these hills, the softness of the sky, the outline of these trees at this very minute lose the illusory meaning with which we had clothed them, henceforth more remote than a lost paradise ... that denseness and that strangeness of the world is absurd.”
—Albert Camus (1913–1960)
“The slanders poured down like Niagara. If you take into consideration the setting—the war and the revolution—and the character of the accused—revolutionary leaders of millions who were conducting their party to the sovereign power—you can say without exaggeration that July 1917 was the month of the most gigantic slander in world history.”
—Leon Trotsky (1879–1940)