The Langlands-Kottwitz approach for some simple Shimura varieties
In a previous paper [Int. Math. Res. Not. 2011, No. 15, 3368--3425 (2011; Zbl 1309.14019)] the author extended techniques of Langlands and Kottwitz to determine the local factors of the Hasse-Weil zeta functions of modular curves at primes of bad reduction. Those methods are extended in this paper to obtain the semisimple Hasse-Weil zeta-function of Shimura varieties associated with unitary groups of real rank \(1\). A key part of the proof is the calculation of the semisimple Lefschetz number in terms of orbital integrals, and thus establishing a special case of a conjecture of Haines and Kottwitz.
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