# Local trace formula

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In [mathematics](/source/Mathematics), the **local trace formula** (Arthur 1991) is a local analogue of the [Arthur–Selberg trace formula](/source/Arthur%E2%80%93Selberg_trace_formula) that describes the character of the representation of *G*(**F**) on the discrete part of *L*2(*G*(**F**)), for *G* a [reductive algebraic group](/source/Reductive_algebraic_group) over a [local field](/source/Local_field) **F**.

## References

- Arthur, James (1991), ["A local trace formula"](http://www.numdam.org/item?id=PMIHES_1991__73__5_0), *[Publications Mathématiques de l'IHÉS](/source/Publications_Math%C3%A9matiques_de_l'IH%C3%89S)*. **73** (73): 5–96, [doi:10.1007/BF02699256](https://doi.org/10.1007/BF02699256). [ISSN 1618-1913](https://www.worldcat.org/issn/1618-1913). MR 1114210. [S2CID 17691368](https://api.semanticscholar.org/CorpusID:17691368)

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