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Atle Selberg
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 Selberg, Sigmund and Henrik Selberg, Henrik, were also mathematicians. His other brother, Arne Selberg, 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 (number theory), partition function as suggested by the works of Ramanujan; however, this result was first published by Hans Rademacher. He studied at the University of Oslo and completed his PhD, doctorate in 1943 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selberg Class
In mathematics, the Selberg class is an axiomatic definition of a class of L-function, ''L''-functions. The members of the class are Dirichlet series which obey four axioms that seem to capture the essential properties satisfied by most functions that are commonly called ''L''-functions or zeta functions. Although the exact nature of the class is conjectural, the hope is that the definition of the class will lead to a classification of its contents and an elucidation of its properties, including insight into their relationship to automorphic forms and the Riemann hypothesis. The class was defined by Atle Selberg in , who preferred not to use the word "axiom" that later authors have employed. Definition The formal definition of the class ''S'' is the set of all Dirichlet series :F(s)=\sum_^\infty \frac absolutely convergent for Re(''s'') > 1 that satisfy four axioms (or assumptions as Selberg calls them): Comments on definition The condition that the real part o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langesund
is the administrative centre of Bamble Municipality in Telemark county, Norway. The town is located on a peninsula along the Langesundsfjorden near the Skaggerak coast. The town of Stathelle lies about to the northwest. The town was established as a ladested in 1765 and on 1 January 1838 it became a self-governing municipality. In 1964, it became part of Bamble Municipality. For a long time, Langesund and neighboring Stathelle have been grouped together as part of the Porsgrunn/Skien metropolitan area and because of this, the population and area data for this town has not been separately tracked by Statistics Norway. What is tracked, is the portion of the metropolitan area located in Bamble Municipality. In 2022, the Langesund/Stathelle area in Bamble measured and together they had a population of 10,276 with a population density of . It is possible to visit the remains of the old Coastal Fortress on Langesundstangen on the extreme end of the Langesund peninsula. The fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selberg Integral
In mathematics, the Selberg integral is a generalization of Euler beta function to ''n'' dimensions introduced by Atle Selberg. Selberg's integral formula When Re(\alpha) > 0, Re(\beta) > 0, Re(\gamma) > -\min \left(\frac 1n , \frac, \frac\right), we have : \begin S_ (\alpha, \beta, \gamma) & = \int_0^1 \cdots \int_0^1 \prod_^n t_i^(1-t_i)^ \prod_ , t_i - t_j , ^\,dt_1 \cdots dt_n \\ & = \prod_^ \frac \end Selberg's formula implies Dixon's identity In mathematics, Dixon's identity (or Dixon's theorem or Dixon's formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating ... for well poised hypergeometric series, and some special cases of Dyson's conjecture. This is a corollary of Aomoto. Aomoto's integral formula Aomoto proved a slightly more general integral formula. With the same conditions as Selberg's formula, : \int_0^1 \cdots \int_0^1 \left( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmund Selberg
Sigmund Selberg (11 August 1910 – 20 April 1994) was a Norwegian mathematician. He was born in Langesund as the son of Ole Michael Ludvigsen Selberg and Anna Kristina Brigtsdatter Skeie. He was twin brother of Arne Selberg and brother of Henrik Selberg and Atle Selberg. He was appointed professor of mathematics at the Norwegian Institute of Technology in Trondheim from 1947 to 1977. His works mainly focused on the distribution of prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...s. References 1910 births 1994 deaths People from Bamble Academic staff of the Norwegian Institute of Technology Norwegian twins 20th-century Norwegian mathematicians Presidents of the Norwegian Mathematical Society {{Norway-academic-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ole Michael Ludvigsen Selberg
Ole Michael Ludvigsen Selberg (7 October 1877 – 11 December 1950) was a Norwegian mathematician and educator. He was born in Flora. He was married to Anna Kristina Brigtsdatter Skeie, and the father of Sigmund, Arne, Henrik and Atle Selberg. His thesis from 1925 treated the theory of algebraic equations. Three of his sons became professors of mathematics, and one was professor of engineering. During the occupation of Norway by Nazi Germany Selberg was a member of the Nazi party Nasjonal Samling. He is also known for his large collection of mathematics literature, which has later been donated to the Norwegian University of Science and Technology The Norwegian University of Science and Technology (NTNU; ) is a public university, public research university in Norway and the largest in terms of enrollment. The university's headquarters is located in Trondheim (city), Trondheim, with region .... References 1877 births 1950 deaths People from Flora, Norway Norwegian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operator (mathematics), operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of System of linear equations, systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter. Mathematical background The name ''spectral theory'' was introduced by David Hilbert in his original formulation of Hilbert space theory, which was cast in terms of quadratic forms in infinitely many variables. The original spectral theorem was therefore conceived as a version of the theorem on Principal axis theorem, principal axes of an ellipsoid, in an infinite-dimensional setting. The later discovery in quantum mechanics t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphic Form
In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms. More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group ''G''(A''F''), for an algebraic group ''G'' and an algebraic number field ''F'', is a complex-valued function on ''G''(A''F'') that is l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gunnerus Medal
The Gunnerus Medal () is a medal awarded by the learned society Royal Norwegian Society of Sciences and Letters. It was inaugurated in 1927, and named after Johan Ernst Gunnerus, founder of the learned society. Members of the learned society are eligible to suggest candidates, and the medal is awarded by the board of directors. Current bearers of the medal are Johannes Moe (since 1988), Stig Strömholm (1997), Olaf I. Rønning (1998), Jørn Sandnes Jørn Sandnes (3 May 1926 – 12 April 2007) was a Norwegian historian. He was born in Snåsa Municipality in Nord-Trøndelag. He was appointed Professor in Trondheim from 1975 to 1992, From 1984 he served as the first rector (academia), recto ... (1999), Gunnar Sundnes (2001), Peder Johan Borgen (2003), Harald A. Øye (2004), Jens Glad Balchen (2006), Olav Smidsrød (2008) and Ivar Giaever (2010). Awardees References Academic awards Norwegian awards Royal Norwegian Society of Sciences and Letters {{award-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. The Wolf Prize includes a monetary award of $100,000. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2024 laureates). Some laureates are counted more than once if they have multiple citizenships. Notes See also * List of mathematics awards References External links * * * Israel-Wolf-Prizes 2015Jerusalempost Wolf Prizes 2017Jerusalempost Wolf Prizes 2018Wolf Prize 2019 {{DEFAULTSORT:Wolf Prize In Mathematics Mathematics Mathematics is a field of study th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields. The Fields Medal is regarded as one of the highest honors a mathematician can receive, and has been list of prizes known as the Nobel or the highest honors of a field, described as the Nobel Prize of Mathematics, although there are several major differences, including frequency of award, number of awards, age limits, monetary value, and award criteria. According to the annual Academic Excellence Survey by Academic Ranking of World Universities, ARWU, the Fields Medal is consistently regarded as the top award in the field of mathematics worldwide, and in another reputation survey conducted by IREG Observatory on Academic Ranking and Excellence, IR ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
