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...

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

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

series, as are the Dirichlet L-functions. 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...

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...

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

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...

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...

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

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...

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

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...

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...

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...

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...

(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...

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...

finite. In particular, if it is finitely generated then it is finite. Selberg's lemma: any finitely generated linear group contains a torsion-free subgroup...

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...

algebras. Selberg's original statement was made only for congruence covers of the modular surface and it has been verified for some small groups. Selberg himself...

theorem represents the beginning of rigorous analytic number theory. Atle Selberg (1949) gave an elementary proof. Dirichlet's theorem is proved by showing...

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

Retrieved 2023-12-13. Ben Green and Terence Tao, Restriction theory of the Selberg sieve, with applications, Journal de Théorie des Nombres de Bordeaux 18...

H\geq T^{1/2+\varepsilon }} was proven by Atle Selberg earlier in 1942. The estimates of Atle Selberg and Karatsuba can not be improved in respect of...