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High Quality Content by WIKIPEDIA articles! In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of G on the space L2(G/ ) of square-integrable functions, where G is a Lie group and a cofinite discrete group. The character is given by the trace of certain functions on G.The simplest case is when is cocompact, when the representation breaks up into discrete summands. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups. When is the cocompact subgroup Z of the real numbers G=R, the Selberg trace formula is essentially the Poisson summation formula.