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.

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