Atle Selberg

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Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950 and an honorary Abel Prize in 2002.

Early years

Selberg was born in Langesund, Norway, the son of teacher Anna Kristina Selberg and mathematician Ole Michael Ludvigsen Selberg. Two of his three brothers, Sigmund and Henrik, were also mathematicians. His other brother, Arne, was a professor of engineering. While he was still at school he was influenced by the work of Srinivasa Ramanujan and he found an exact analytical formula for the partition function as suggested by the works of Ramanujan; however, this result was first published by Hans Rademacher.

He studied at the

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 ${\displaystyle \Re (s)={\tfrac {1}{2}}}$.

During the war, he fought against the German invasion of Norway, and was imprisoned several times.

Post-war in Norway

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 1948 Selberg submitted two papers in Annals of Mathematics in which he proved by elementary means the theorems for primes in arithmetic progression and the density of primes.^[2][3] This challenged the widely held view of his time that certain theorems are only obtainable with the advanced methods of complex analysis. Both results were based on his work on the asymptotic formula

${\displaystyle \vartheta \left(x\right)\log \left(x\right)+\sum \limits _{p\leq x}{\log \left(p\right)}\vartheta \left({\frac {x}{p}}\right)=2x\log \left(x\right)+O\left(x\right)}$

where

${\displaystyle \vartheta \left(x\right)=\sum \limits _{p\leq x}{\log \left(p\right)}}$

for primes ${\displaystyle p}$. He established this result by elementary means in March 1948, and by July of that year, Selberg and

For his fundamental accomplishments during the 1940s, Selberg received the 1950 Fields Medal.

Institute for Advanced Study

Selberg moved to the United States and worked as an associate professor at

He generally worked alone. His only coauthor was Sarvadaman Chowla.^[8][9]

Selberg was awarded the 1986 Wolf Prize in Mathematics. He was also awarded an honorary Abel Prize in 2002, its founding year, before the awarding of the regular prizes began.

Selberg received many distinctions for his work, in addition to the Fields Medal, the Wolf Prize and the Gunnerus Medal. He was elected to the Norwegian Academy of Science and Letters, the Royal Danish Academy of Sciences and Letters and the American Academy of Arts and Sciences.

In 1972, he was awarded an honorary degree, doctor philos. honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology.^[10]

His first wife, Hedvig, died in 1995. With her, Selberg had two children: Ingrid Selberg (married to playwright Mustapha Matura) and Lars Selberg. In 2003 Atle Selberg married Betty Frances ("Mickey") Compton (born in 1929).

He died at home in Princeton, New Jersey on 6 August 2007 of heart failure. Upon his death he was survived by his widow, daughter, son, and four grandchildren.^[11]

Selected publications

Selberg's collected works were published in two volumes. The first volume contains 41 articles, and the second volume contains three additional articles, in addition to Selberg's lectures on sieves.

• Selberg, Atle (1989). Collected Papers. Volume I. Berlin, Heidelberg:
  ISBN 9783642410215.^[12] Description at M.I.T. Press Bookstore
• Selberg, Atle (1991). Collected Papers. Volume II. Berlin, Heidelberg:
  Zbl 0729.11001. Description at M.I.T. Press Bookstore

References

1. ^ ^{a b} Ferrara, Christine (9 August 2007). "Atle Selberg 1917–2007". Institute for Advanced Study (Press release). Retrieved 14 October 2020.
2. S2CID 124153092. Archived
   (PDF) from the original on 9 October 2022.
3. ^ Selbert, Atle (April 1949). "An Elementary Proof of Dirichlet's Theorem About Primes in Arithmetic Progression". Annals of Mathematics. 50 (2): 297–304.
   JSTOR 1969454
   .
4. S2CID 15408261. Archived
   (PDF) from the original on 9 October 2022.
5. ^ Goldfeld, Dorian (2003). "The Elementary Proof of the Prime Number Theorem: an Historical Perspective" (PDF). Number Theory: New York Seminar: 179–192. Archived (PDF) from the original on 9 October 2022.
6. doi:10.1090/S0273-0979-08-01223-8. Archived
   (PDF) from the original on 9 October 2022.
7. ^ Maugh II, Thomas H. (22 August 2007). "Atle Selberg, 90; Researcher 'Left a Profound Imprint on the World of Mathematics'". Los Angeles Times. Retrieved 14 October 2020.
8. PMID 16588908
   .
9. ^ Conrey, Brian (12 March 2020). "Math Encounters - Primes and Zeros: A Million-Dollar Mystery". National Museum of Mathematics, YouTube. (See 58:30 of 1:18:02 in video.)
10. ^ "Honorary Doctors". Norwegian University of Science and Technology.
11. ^ Pearce, Jeremy (17 August 2007). "Atle Selberg, 90, Lauded Mathematician, Dies". The New York Times.
12. ^ Berg, Michael (7 October 2014). "review of Collected Papers I: Atle Helberg". MAA Reviews, Mathematical Association of America (MAA).

Further reading

• Albers, Donald J. and
  ISBN 978-0-691-14829-8
  .
• Baas, Nils A.; Skau, Christian F. (2008). "The lord of the numbers, Atle Selberg. On his life and mathematics". Bull. Amer. Math. Soc. 45 (4): 617–649.
  doi:10.1090/S0273-0979-08-01223-8
  . Interview with Selberg
• Hejhal, Dennis (June–July 2009). "Remembering Atle Selberg, 1917–2007" (PDF). Notices of the American Mathematical Society. 56 (6): 692–710.
• Selberg (1996). "Reflections Around the Ramanujan Centenary" (PDF). Resonance. 1 (12): 81–91.
  S2CID 120285506. Archived
  (PDF) from the original on 9 October 2022.

External links

Wikimedia Commons has media related to Atle Selberg.

Wikiquote has quotations related to Atle Selberg.

• Atle Selberg at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Atle Selberg", MacTutor History of Mathematics Archive, University of St Andrews
• Atle Selberg archive webpage
• Obituary at Institute for Advanced Study
• Obituary in The Times
• Atle Selbergs private archive exists at NTNU University Library