An alternating sum formula for multiplicities in 𝐿²(Γ\𝐺)

Miatello, Roberto J.

doi:10.1090/S0002-9947-1982-0637710-0

An alternating sum formula for multiplicities in $L^{2}(\Gamma \backslash G)$
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by Roberto J. Miatello

Trans. Amer. Math. Soc. 269 (1982), 567-574

DOI: https://doi.org/10.1090/S0002-9947-1982-0637710-0

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Abstract:

We prove an alternating sum formula for multiplicities in ${L^2}(\Gamma \backslash G)$, where $G$ is a semisimple Lie group of split rank one with finite center and $\Gamma$ is a discrete cocompact torsion free subgroup.

References

David L. DeGeorge and Nolan R. Wallach, Limit formulas for multiplicities in $L^{2}(\Gamma \backslash G)$. II. The tempered spectrum, Ann. of Math. (2) 109 (1979), no. 3, 477–495. MR 534759, DOI 10.2307/1971222
Harish-Chandra, The characters of semisimple Lie groups, Trans. Amer. Math. Soc. 83 (1956), 98–163. MR 80875, DOI 10.1090/S0002-9947-1956-0080875-7
Harish-Chandra, Harmonic analysis on real reductive groups. III. The Maass-Selberg relations and the Plancherel formula, Ann. of Math. (2) 104 (1976), no. 1, 117–201. MR 439994, DOI 10.2307/1971058
R. Hotta and R. Parthasarathy, Multiplicity formulae for discrete series, Invent. Math. 26 (1974), 133–178. MR 348041, DOI 10.1007/BF01435692
A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
Serge Lang, $\textrm {SL}_{2}(\textbf {R})$, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. MR 0430163
Roberto J. Miatello, The Minakshisundaram-Pleijel coefficients for the vector-valued heat kernel on compact locally symmetric spaces of negative curvature, Trans. Amer. Math. Soc. 260 (1980), no. 1, 1–33. MR 570777, DOI 10.1090/S0002-9947-1980-0570777-5
Wilfried Schmid, On a conjecture of Langlands, Ann. of Math. (2) 93 (1971), 1–42. MR 286942, DOI 10.2307/1970751
Nolan R. Wallach, On the Selberg trace formula in the case of compact quotient, Bull. Amer. Math. Soc. 82 (1976), no. 2, 171–195. MR 404533, DOI 10.1090/S0002-9904-1976-13979-1