In mathematics, the Selberg class is an axiomatic definition of a class of L-functions. The members of the class are Dirichlet series which obey four axioms...

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...

showed that a suitable analog of the Selberg trace formula for the action of the idèle class group on the adèle class space would imply the Riemann hypothesis...

term L-function here includes many known types of zeta functions. The Selberg class is an attempt to capture the core properties of L-functions in a set...

s) denotes the Dirichlet series of u(n). It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named...

conjecture Riemann hypothesis and the generalized Riemann hypothesis. Selberg class S Explicit formulae for L-functions Trace formula A directory of all...

Q, and Δ its discriminant. Artin's conjecture Dirichlet L-function Selberg class Grand Riemann hypothesis Davenport, Harold (2000). Multiplicative Number...

In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group...

In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over...

-Li coefficients. A. Droll generalized the results to the extended Selberg class, A. Bucur, A.-M. Ernvall-Hytönen, A. Odžak and L. Smajlović investigated...

In mathematics, the Chowla–Selberg formula is the evaluation of a certain product of values of the gamma function at rational values in terms of values...

The Selberg zeta-function was introduced by Atle Selberg (1956). It is analogous to the famous Riemann zeta function ζ ( s ) = ∏ p ∈ P 1 1 − p − s {\displaystyle...

all arise as automorphic L-functions, and hence should be part of the Selberg class. There are also conjectures concerning the values of these L-functions...

of L-functions, and in particular are expected to coincide with the Selberg class. Furthermore, all L-functions over arbitrary number fields are widely...

(Martian crater) List of things named after Niels Henrik Abel Abel Prize Selberg class Weather forecasting Aanderaa–Karp–Rosenberg conjecture "Niels Henrik...

Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg formula Hasse–Weil zeta function...

of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein only a few residue classes are removed. The...

non-commutative harmonic analysis, the idea is taken even further in the Selberg trace formula but takes on a much deeper character. A series of mathematicians...

associated with quadratic extensions of the rationals by class field theory. In this case Selberg's trace formula shows that the spectrum of the Laplacian...

conversation with Landau, there was little basis for such speculation. However Selberg in the early 1950s proved a duality between the length spectrum of a Riemann...

Drinfeld, formule des traces d'Arthur-Selberg et correspondance de Langlands." (Drinfeld shtukas, Arthur-Selberg trace formula and Langlands correspondence)...

(443,449), (457,463), (461,467). D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive...

the greatest mathematician of the first half of the 20th century. Atle Selberg said of Siegel and his work: He was in some ways, perhaps, the most impressive...

the original on 8 April 2022. Retrieved 7 April 2019. "Remembering Atle Selberg, 1917–2007" (PDF). Ams.org. Archived (PDF) from the original on 23 November...

overview of the subject of group representations. See Selberg trace formula and the Arthur-Selberg trace formula for generalizations to discrete cofinite...

Selberg. However, the circumstances leading up to the proofs, as well as publication disagreements, led to a bitter dispute between Erdős and Selberg...

Selberg, A. "On Epstein's Zeta-Function". EuDML. pp. 86–110. Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng (6 June 1997). "Ramanujan's class invariants...

the existence of cusp forms led to the disproof of a conjecture of Atle Selberg. He has obtained the strongest known bounds towards the Ramanujan–Petersson...

of the Erdős–Selberg proof of the PNT. This was the first machine-verified proof of the PNT. Avigad chose to formalize the Erdős–Selberg proof rather...