Atle Selberg

Atle Selberg
Name	Atle Selberg
Caption	Atle Selberg in 1987
Birth date	14 June 1917
Birth place	Langesund, Norway
Death date	06 August 2007
Death place	Princeton, New Jersey, United States
Fields	Mathematics
Workplaces	Institute for Advanced Study
Alma mater	University of Oslo
Doctoral advisor	Carl Størmer
Known for	Selberg trace formula, Selberg zeta function, Elementary proof of the prime number theorem
Prizes	Fields Medal (1950), Wolf Prize in Mathematics (1986)

Atle Selberg was a preeminent Norwegian mathematician whose profound contributions fundamentally shaped modern analytic number theory and automorphic forms. His career, spent largely at the Institute for Advanced Study in Princeton, New Jersey, was marked by deep and original insights that bridged number theory and spectral theory. He is best known for the revolutionary Selberg trace formula and the eponymous Selberg zeta function, work for which he was awarded the Fields Medal.

Early life and education

Born in Langesund, his early talent was nurtured by reading the works of Srinivasa Ramanujan and other giants. He enrolled at the University of Oslo, where he was significantly influenced by the number theorist Carl Størmer. Even before completing his doctorate, he made his first major discovery, deriving an asymptotic formula for the zeros of Riemann zeta function on the critical line. His doctoral dissertation, completed during the Second World War, further established his formidable reputation in the field.

Career and research

After the war, his growing fame led to an invitation to the Institute for Advanced Study, where he became a permanent member in 1951, joining luminaries like Albert Einstein and John von Neumann. His research spanned the Riemann hypothesis, discrete groups, and modular forms. A landmark achievement was his elementary proof of the prime number theorem, developed independently of and contemporaneously with Paul Erdős, which avoided the deep machinery of complex analysis used in the earlier proofs by Jacques Hadamard and Charles Jean de la Vallée-Poussin.

Selberg trace formula

This monumental discovery, presented in 1956, established a deep duality between the geometry of Riemann surfaces and their spectral properties. The formula relates the Laplace spectrum of a hyperbolic surface to the lengths of its closed geodesics. It became a foundational tool in quantum chaos and the study of arithmetic groups, influencing subsequent work by mathematicians like Robert Langlands and Dennis Hejhal.

Selberg zeta function

Intimately connected to his trace formula, this function is defined for a hyperbolic surface in terms of its primitive closed geodesics. It encodes profound geometric and spectral information, sharing formal properties with the classical Riemann zeta function. The Selberg zeta function has become central to the study of dynamical systems and the connection between number theory and physics, particularly in areas like quantum field theory.

Awards and honors

His contributions were recognized with the highest honors in mathematics. He received the Fields Medal at the International Congress of Mathematicians in 1950. Later accolades included the Wolf Prize in Mathematics in 1986, which he shared with Samuel Eilenberg. He was a member of the Norwegian Academy of Science and Letters, the Royal Swedish Academy of Sciences, and a foreign member of both the Royal Society and the National Academy of Sciences.

Personal life and legacy

Known for his intense independence and preference for solitary work, he was nonetheless a dedicated teacher and colleague. He remained at the Institute for Advanced Study until his retirement, profoundly influencing generations of mathematicians through his lectures and published work. His techniques and vision continue to permeate analytic number theory, spectral theory, and ergodic theory, ensuring his legacy as one of the most original mathematical thinkers of the twentieth century.

Category:Norwegian mathematicians Category:Fields Medal winners Category:Wolf Prize in Mathematics laureates