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Atle Selberg

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Atle Selberg (June 14, 1917 – August 6, 2007) was a prominent Norwegian mathematician renowned for his profound contributions to analytic number theory and related fields. His innovative work has had a lasting impact on mathematics, particularly in the areas of prime number theory, automorphic forms, and spectral theory.


Key Contributions:



  1. Selberg Sieve:

  2. Overview: Selberg developed the Selberg sieve, a powerful generalization of the sieve of Eratosthenes.


  3. Impact: This tool became fundamental in analytic number theory for estimating the distribution of prime numbers and studying sifted sets of integers.




  4. Elementary Proof of the Prime Number Theorem:



  5. Achievement: In 1949, Selberg provided an "elementary" proof of the prime number theorem independently and concurrently with Paul Erdős.


  6. Significance: Their proofs avoided complex analysis, which was previously thought essential, thus opening new avenues in number theory.




  7. Selberg Trace Formula:



  8. Description: One of his most celebrated contributions, the Selberg trace formula creates a deep link between the lengths of closed geodesics on a Riemann surface and the eigenvalues of the Laplacian operator.


  9. Applications: This formula is a cornerstone in the study of automorphic forms and has profound implications in quantum chaos and spectral geometry.




  10. Work on Zeta Functions and Automorphic Forms:



  11. Research: Selberg made significant advances in understanding zeta functions associated with automorphic forms.

  12. Contribution: His insights contributed to the development of the Langlands program, a set of far-reaching conjectures connecting number theory and representation theory.


Career Highlights:



  • Institute for Advanced Study (IAS):

  • Selberg spent a significant part of his career at the IAS in Princeton, New Jersey.


  • At the IAS, he collaborated with other leading mathematicians and mentored emerging scholars.




  • Fields Medal (1950):




  • He was awarded the Fields Medal, one of the highest honors in mathematics, recognizing his contributions to number theory and the theory of automorphic forms.




  • Other Honors:



  • Wolf Prize in Mathematics (1986): For his work in number theory and automorphic forms.

  • Honorary Degrees: Received honorary doctorates from several universities worldwide.


Legacy:


Atle Selberg's work continues to influence modern mathematics profoundly. His methods and results are integral to ongoing research in number theory, mathematical physics, and representation theory. The tools he developed are still used by mathematicians to tackle some of the most challenging problems in the field.


Further Reading:



  • Publications: Selberg authored numerous papers, many of which are considered seminal works in mathematics.

  • Collected Works: His collected papers have been published, providing valuable insights into his thought processes and methodologies.


Personal Life:



  • Early Years: Born in Langesund, Norway, Selberg showed an early aptitude for mathematics.

  • Education: He studied at the University of Oslo, where he completed his Ph.D. under the supervision of Ernst Selmer.


Atle Selberg is remembered not only for his exceptional mathematical intellect but also for his modesty and dedication to the advancement of mathematics.

All published works
Action Title Year Authors
+ Sección a cargo de Ana Jeremías López y Leovigildo Alonso Tarrío 2008 Atle Selberg
Fernando Chamizo Lorente
+ On an Elementary Method in the Theory of Primes 2002 Atle Selberg
+ Reflections around the Ramanujan centenary 2001 Atle Selberg
+ Reflections around the Ramanujan centenary 1996 Atle Selberg
+ Number Theory, Trace Formulas, and Discrete Groups: Symposium in Honor of Atle Selberg, Oslo, Norway, July 14-21, 1987 1989 Atle Selberg
Karl Egil Aubert
Enrico Bombieri
Dorian Goldfeld
+ Remarks on multiplicative functions 1977 Atle Selberg
+ Sieve methods 1971 Atle Selberg
+ Recent developments in the theory of discontinuous groups of motions of symmetric spaces 1969 Atle Selberg
+ ADVANCED MATHEMATICAL RESEARCH 1968 Atle Selberg
+ On Epstein's Zeta-function. 1967 S. Chowla
Atle Selberg
+ On the estimation of Fourier coefficients of modular forms 1965 Atle Selberg
+ Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series 1956 Atle Selberg
+ Note on a Paper By L. G. Sathe 1954 Atle Selberg
+ PDF An Elementary Proof of the Prime-Number Theorem for Arithmetic Progressions 1950 Atle Selberg
+ PDF On Epstein's Zeta Function (I) 1949 S. Chowla
Atle Selberg
+ An Elementary Proof of the Prime-Number Theorem 1949 Atle Selberg
+ An Elementary Proof of Dirichlet's Theorem About Primes in an Arithmetic Progression 1949 Atle Selberg
+ On the zeros of Riemann's zeta-function 1943 Atle Selberg
Common Coauthors
Coauthor Papers Together
S. Chowla 2
Enrico Bombieri 1
Karl Egil Aubert 1
Dorian Goldfeld 1
Fernando Chamizo Lorente 1
Commonly Cited References
Action Title Year Authors # of times referenced
+ ON THE REPRESENTATION OF A LARGER EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES 1973 Chen Jing-Run
 1
+ Lectures on Elementary Number Theory 1977 Hans Rademacher
 1
+ Elementare Beweise des Primzahlsatzes mit Restglied. II. 1964 Eduard Wirsing
 1
+ �ber eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichlet scher Reihen durch Funktionalgleichungen 1949 Hans Maaß
 1
+ On the First Betti Number of Compact Quotient Spaces of Higher-Dimensional Symmetric Spaces 1962 YOZÔ MATSUSHIMA
 1
+ On Discrete Subgroups of Lie Groups 1960 André Weil
 1
+ Formule de Poisson pour les vari�t�s riemanniennes 1974 Jacques Chazarain
 1
+ An elementary proof of the prime number theorem with a remainder term 1970 Harold G. Diamond
J. Steinig
 1
+ PDF FUNDAMENTAL DOMAINS FOR LATTICES IN RANK ONE SEMISIMPLE LIE GROUPS 1969 Howard Garland
M. S. Raghunathan
 1
+ PDF On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem 1949 P. Erdős
 1
+ Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms 1968 G. D. Mostow
 1
+ On the spectrum of positive elliptic operators and periodic bicharacteristics 1975 J. J. Duistermaat
Victor Guillemin
 1
+ Differential Geometry and Symmetric Spaces 2001 Sigurđur Helgason
 1
+ On Epstein's Zeta-function. 1967 S. Chowla
Atle Selberg
 1
+ Spectral Methods of Automorphic Forms 2002 Henryk Iwaniec
 1
+ PDF Arithmetic Subgroups of Algebraic Groups 1962 Armand Borel
Harish-chandra Harish-Chandra
 1
+ An Elementary Proof of the Prime-Number Theorem 1949 Atle Selberg
 1
+ An Elementary Proof of Dirichlet's Theorem About Primes in an Arithmetic Progression 1949 Atle Selberg
 1
+ On Compact, Locally Symmetric Kahler Manifolds 1960 Eugenio Calabi
Edoardo Vesentini
 1
+ PDF The zeros of Riemann's zeta-function on the critical line 1921 G. H. Hardy
J. E. Littlewood
 1
+ Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series 1956 Atle Selberg
 1
+ Analytic number theory 1998 Donald J. Newman
 1
+ La funció / de Riemann 2007 Jordi Quer Bosor
 1
+ PDF On compact, Riemannian manifolds with constant curvature. I 1961 Eugenio Calabi
 1
+ The Elementary Proof of the Prime Number Theorem: An Historical Perspective 2004 Dorian Goldfeld
 1
+ Analytic Number Theory 2004 Henryk Iwaniec
Emmanuel Kowalski
 1
+ On the zeros of Riemann's zeta-function 1943 Atle Selberg
 1
+ PDF Sieving by prime powers 1974 Patricia M. Gallagher
 1