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...

formulated a trace formula that is actually equivalent to the Riemann hypothesis. This strengthened the analogy with the Selberg trace formula to the point...

Trace formula may refer to: Arthur–Selberg trace formula, also known as invariant trace formula, Jacquet's relative trace formula, simple trace formula...

Poisson summation formula is the archetype for vast developments in harmonic analysis and number theory. The Selberg trace formula was later generalized...

theory into number theory, culminating in his development of the Selberg trace formula, the most famous and influential of his results. In its simplest...

In mathematics, the local trace formula (Arthur 1991) is a local analogue of the Arthur–Selberg trace formula that describes the character of the representation...

s_{0}/2} , and hence the Selberg zeta-function has a zero at s 0 / 2 {\displaystyle s_{0}/2} .[citation needed] Selberg trace formula Fischer, Jürgen (1987)...

The Selberg trace formula is the analogue for these functions of the explicit formulas in prime number theory. Selberg proved that the Selberg zeta functions...

for a total of 890 pages. 1983 Selberg trace formula. Hejhal's proof of a general form of the Selberg trace formula consisted of 2 volumes with a total...

found an example that shows the formula may be interpreted as a sort of the Selberg trace formula. A proof of the formula in the context of the six operations...

Urakawa, C. Gordon). In particular Vignéras (1980), based on the Selberg trace formula for PSL(2,R) and PSL(2,C), constructed examples of isospectral,...

local fields. Arthur’s work, which was motivated by the Arthur–Selberg trace formula, suggests a framework for understanding complex relationships in...

Hejhal works on analytic number theory, automorphic forms, the Selberg trace formula and quantum chaos. From 1972 to 1974 he was a Sloan Fellow. In 1986...

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...

 section 16) in their book Automorphic Forms on GL(2) using the Selberg trace formula. It was one of the first examples of the Langlands philosophy that...

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

(2005), who derived the explicit formula of Weil via harmonic analysis on adelic spaces. Selberg trace formula Selberg zeta function The original prime...

Drinfeld, formule des traces d'Arthur-Selberg et correspondance de Langlands. [Drinfelʹd shtukas, Arthur-Selberg trace formula and Langlands correspondence]...

years around 1960, in creating such a theory. The theory of the Selberg trace formula, as applied by others, showed the considerable depth of the theory...

conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands program modularity...

of the Selberg trace formula, Journal of Soviet Mathematics, vol. 8, 1977, pp. 171–199 Spectral theory of automorphic functions, the Selberg zeta-function...

theorem Theorem of the three geodesics Curve-shortening flow Selberg trace formula Selberg zeta function Zoll surface Besse, A.: "Manifolds all of whose...

and Petersson formulae from the classical setup. While the usual Selberg trace formula, as well as its generalizations due to James Arthur, consists in...

and the Selberg trace formula". Journal of Functional Analysis. 53 (2): 151–201. doi:10.1016/0022-1236(83)90050-2. (See Selberg trace formula.) Connes...

classes of solvable Lie groups, a very detailed theory is available. Selberg trace formula Langlands program Kirillov orbit theory Discrete series representation...

automorphic forms: for example all modern treatments of the Arthur–Selberg trace formula are done in this adélic setting. The modular group is usually defined...

Further results are conditional on improved forms of the Arthur–Selberg trace formula. Harris has a conditional proof of a result for the product of two...

Gurevich-Segal). Bump, Daniel (1989), "The Rankin-Selberg method: a survey", Number theory, trace formulas and discrete groups (Oslo, 1987), Boston, MA: Academic...

conjectures using the Arthur–Selberg trace formula, but in order for this approach to work, the geometric sides of the trace formula for different groups must...