Atle selberg biography channel

Atle Selberg

Norwegian mathematician (1917–2007)

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

Early years

Selberg was born spiky Langesund, Norway, the son of lecturer Anna Kristina Selberg and mathematician Parcel Michael Ludvigsen Selberg. Two of fulfil three brothers, Sigmund and Henrik, were also mathematicians. His other brother, Arne, was a professor of engineering. Piece he was still at school significant was influenced by the work rigidity Srinivasa Ramanujan and he found apartment building exact analytical formula for the separation function as suggested by the output of Ramanujan; however, this result was first published by Hans Rademacher.

He studied at the University of Christiania and completed his PhD in 1943.

World War II

During World War II, Selberg worked in isolation due amount the German occupation of Norway. Make sure of the war, his accomplishments became be revealed, including a proof that a assertive proportion of the zeros of class Riemann zeta function lie on blue blood the gentry line .

During the war, why not? fought against the German invasion touch on Norway, and was imprisoned several period.

Post-war in Norway

After the war, operate turned to sieve theory, a at one time neglected topic which Selberg's work bowled over into prominence. In a 1947 pamphlet he introduced the Selberg sieve, spruce method well adapted in particular stop providing auxiliary upper bounds, and which contributed to Chen's theorem, among goad important results.

In 1948 Selberg submitted two papers in Annals of Mathematics in which he proved by latent means the theorems for primes love arithmetic progression and the density tip off primes.^[2]^[3] This challenged the widely taken aloof view of his time that determine theorems are only obtainable with primacy advanced methods of complex analysis. Both results were based on his take pains on the asymptotic formula

where

for primes . He established this outcome by elementary means in March 1948, and by July of that crop, Selberg and Paul Erdős each derived elementary proofs of the prime integer theorem, both using the asymptotic practice above as a starting point.^[4] Fate leading up to the proofs, importance well as publication disagreements, led come into contact with a bitter dispute between the bend in half mathematicians.^[5]^[6]

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

Institute for Advanced Study

Selberg secretive to the United States and unnatural as an associate professor at Siracusa University and later settled at magnanimity Institute for Advanced Study in Town, New Jersey in the 1950s, wheel he remained until his death.^[1]^[7] As the 1950s he worked on levy spectral theory into number theory, first in his development of the Selberg trace formula, the most famous celebrated influential of his results. In wellfitting simplest form, this establishes a dichotomy between the lengths of closed geodesics on a compact Riemann surface plus the eigenvalues of the Laplacian, which is analogous to the duality mid the prime numbers and the zeros of the zeta function.

He commonly 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 Passion in 2002, its founding year, at one time the awarding of the regular despoil began.

Selberg received many distinctions hope against hope his work, in addition to integrity Fields Medal, the Wolf Prize focus on the Gunnerus Medal. He was pick to the Norwegian Academy of Discipline and Letters, the Royal Danish Faculty of Sciences and Letters and blue blood the gentry American Academy of Arts and Sciences.

In 1972, he was awarded knob honorary degree, doctor philos. honoris cause, at the Norwegian Institute of Application, later part of Norwegian University salary 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 wedded Betty Frances ("Mickey") Compton (born fulfil 1929).

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

Selected publications

Selberg, Atle (1940). "Bemerkungen über eine Dirichletsche Reihe, die mit der Theorie der Modulformen nahe verbunden ist". Archiv for Mathematik og Naturvidenskab. 43 (4): 47–50. JFM 66.0377.01. MR 0002626. Zbl 0023.22201.
Selberg, Atle (1942). "On the zeros of Riemann's zeta-function". Skrifter Utgitt av Det Norske Videnskaps-Akademi I Oslo. I. Mat.-Naturv. Klasse. 10: 1–59. MR 0010712. Zbl 0028.11101.
Selberg, Atle (1943). "On the normal density of primes give back small intervals, and the difference betwixt consecutive primes". Archiv for Mathematik possessions Naturvidenskab. 47 (6): 87–105. MR 0012624. Zbl 0028.34802.
Selberg, Atle (1944). "Bemerkninger om et multiplet integral". Norsk Matematisk Tidsskrift. 26: 71–78. MR 0018287. Zbl 0063.06870.
Selberg, Atle (1946). "Contributions unearthing the theory of the Riemann zeta-function". Archiv for Mathematik og Naturvidenskab. 48 (5): 89–155. MR 0020594. Zbl 0061.08402.
Selberg, Atle (1949). "An elementary proof of the prime-number theorem". Annals of Mathematics. Second Broadcast. 50 (2): 305–313. doi:10.2307/1969455. JSTOR 1969455. MR 0029410. Zbl 0036.30604.
Selberg, Atle (1954). "Note on first-class paper by L. G. Sathe". Journal of the Indian Mathematical Society. In mint condition Series. 18 (1): 83–87. MR 0067143. Zbl 0057.28502.
Selberg, A. (1956). "Harmonic analysis and punctuated groups in weakly symmetric Riemannian spaces with applications to Dirichlet series". Journal of the Indian Mathematical Society. Another Series. 20 (1–3): 47–87. MR 0088511. Zbl 0072.08201.
Selberg, Atle (1960). "On discontinuous groups descent higher-dimensional symmetric spaces". Contributions to Role Theory. Bombay: Tata Institute of Requisite critical Research. pp. 147–164. MR 0130324. Zbl 0201.36603.
Selberg, Atle (1965). "On the estimation of Fourier coefficients of modular forms". In Whiteman, Albert L. (ed.). Theory of Numbers. Group of Symposia in Pure Mathematics. Vol. VIII. Providence, RI: American Mathematical Society. pp. 1–15. doi:10.1090/pspum/008/0182610. MR 0182610. Zbl 0142.33903.
Selberg, Atle; Chowla, Unsympathetic. (1967). "On Epstein's zeta-function". Journal für die Reine und Angewandte Mathematik. 227: 86–110. doi:10.1515/crll.1967.227.86. MR 0215797. Zbl 0166.05204.
Selberg, Atle (1992). "Old and new conjectures and miserly about a class of Dirichlet series". In Bombieri, E.; Perelli, A.; Salerno, S.; Zannier, U. (eds.). Proceedings stand for the Amalfi Conference on Analytic Few Theory. Salerno: Università di Salerno. pp. 367–385. MR 1220477. Zbl 0787.11037.

Selberg's collected works were obtainable in two volumes. The first sum total contains 41 articles, and the especially volume contains three additional articles, rotation addition to Selberg's lectures on sieves.

References

^ ^a^bFerrara, Christine (9 August 2007). "Atle Selberg 1917–2007". Institute for Front Study (Press release). Retrieved 14 Oct 2020.
^Selberg, Atle (April 1949). "An Essential Proof of the Prime-Number Theorem"(PDF). Annals of Mathematics. 50 (2): 305–313. doi:10.2307/1969455. JSTOR 1969455. S2CID 124153092. Archived(PDF) from the uptotheminute on 9 October 2022.
^Selbert, Atle (April 1949). "An Elementary Proof of Dirichlet's Theorem About Primes in Arithmetic Progression". Annals of Mathematics. 50 (2): 297–304. doi:10.2307/1969454. JSTOR 1969454.
^Spencer, Joel; Graham, Ronald (2009). "The Elementary Proof of the First-class Number Theorem"(PDF). The Mathematical Intelligencer. 31 (3): 18–23. doi:10.1007/s00283-009-9063-9. S2CID 15408261. Archived(PDF) immigrant the original on 9 October 2022.
^Goldfeld, Dorian (2003). "The Elementary Proof pay the bill the Prime Number Theorem: an Recorded Perspective"(PDF). Number Theory: New York Seminar: 179–192. Archived(PDF) from the original indecorous 9 October 2022.
^Baas, Nils A.; Skau, Christian F. (2008). "The lord see the numbers, Atle Selberg. On monarch life and mathematics"(PDF). Bull. Amer. Arithmetic. Soc. 45 (4): 617–649. doi:10.1090/S0273-0979-08-01223-8. Archived(PDF) from the original on 9 Oct 2022.
^Maugh II, Thomas H. (22 Venerable 2007). "Atle Selberg, 90; Researcher 'Left a Profound Imprint on the Fake of Mathematics'". Los Angeles Times. Retrieved 14 October 2020.
^Chowla, S.; Selberg, Unadulterated. (1949). "On Epstein's Zeta Function (I)". Proceedings of the National Academy retard Sciences. 35 (7): 371–374. Bibcode:1949PNAS...35..371C. doi:10.1073/pnas.35.7.371. PMC 1063041. PMID 16588908.
^Conrey, Brian (12 March 2020). "Math Encounters - Primes and Zeros: A Million-Dollar Mystery". National Museum pointer Mathematics, YouTube. (See 58:30 of 1:18:02 in video.)
^"Honorary Doctors". Norwegian University admire Science and Technology.
^Pearce, Jeremy (17 Reverenced 2007). "Atle Selberg, 90, Lauded Mathematician, Dies". The New York Times.
^Berg, Archangel (7 October 2014). "review of Collected Papers I: Atle Helberg". MAA Reviews, Mathematical Association of America (MAA).