Arthur–Selberg trace formula, also known as invariant trace formula, Jacquet's relative trace formula, simple trace formula, stable trace formula
Grothendieck trace formula, an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology, used to express the Hasse–Weil zeta function.
Gutzwiller trace formula: See Quantum chaos
Kuznetsov trace formula, an extension of the Petersson trace formula.
Local trace formula, an analog of Arthur–Selberg trace formula
Petersson trace formula
Selberg trace formula
Behrend's trace formula, or Behrend's fixed point formula a generalization of the Grothendieck–Lefschetz trace formula, that may be interpreted as a Selberg trace formula.
In mathematics, the Selberg traceformula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group...
geometry, the Grothendieck traceformula expresses the number of points of a variety over a finite field in terms of the trace of the Frobenius endomorphism...
number theory, the Kuznetsov traceformula is an extension of the Petersson traceformula. The Kuznetsov or relative traceformula connects Kloosterman sums...
non-commutative harmonic analysis, the idea is taken even further in the Selberg traceformula, but takes on a much deeper character. A series of mathematicians applying...
In mathematics, the local traceformula (Arthur 1991) is a local analogue of the Arthur–Selberg traceformula that describes the character of the representation...
density of states which is the trace of the semiclassical Green's function and is given by the Gutzwiller traceformula: g c ( E ) = ∑ k T k ∑ n = 1 ∞...
In analytic number theory, the Petersson traceformula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a...
H\subset G} be a subgroup. While the usual traceformula studies the harmonic analysis on G, the relative traceformula is a tool for studying the harmonic analysis...
(b)\right)} where tr {\displaystyle \operatorname {tr} } is the matrix trace and diag ( a ) {\displaystyle \operatorname {diag} (a)} is the diagonal...
introduced by Robert Langlands (1979, 1983) in his work on the stable traceformula. Roughly speaking, an endoscopic group H of G is a quasi-split group...
{\displaystyle \pi _{1}(G)} . This is a (conjectural) version of the Lefschetz traceformula for Bun G ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} when X...
Urakawa, C. Gordon). In particular Vignéras (1980), based on the Selberg traceformula for PSL(2,R) and PSL(2,C), constructed examples of isospectral, non-isometric...
Banach spaces. The theorem should not be confused with the Grothendieck traceformula from algebraic geometry. Given a Banach space ( B , ‖ ⋅ ‖ ) {\displaystyle...
geodesics rather than primes. The Selberg traceformula is the analogue for these functions of the explicit formulas in prime number theory. Selberg proved...
for a total of 890 pages. 1983 Selberg traceformula. Hejhal's proof of a general form of the Selberg traceformula consisted of 2 volumes with a total length...
denominator of the Weyl character formula vanish to high order at the identity element, so it is necessary to take a limit of the trace of an element tending to...
theory into number theory, culminating in his development of the Selberg traceformula, the most famous and influential of his results. In its simplest form...
mechanics in chaotic systems. In that context, he developed the Gutzwiller traceformula, the main result of periodic orbit theory, which gives a recipe for...
the subject of group representations. See Selberg traceformula and the Arthur-Selberg traceformula for generalizations to discrete cofinite subgroups...
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