Multiplicity formulas for discrete series representations in.

Abstract: Let denote the split symplectic group of rank 2 over . Fix a prime p. Let be a parahoric subgroup of . An arithmetic subgroup Γ is defined by , where . In this paper, we calculate Arthurʼs -Lefschetz trace formula for in order to obtain an explicit formula for multiplicities of discrete series and some non-tempered unitary representations in the discrete spectrum of for each such Γ. From them we derive explicit multiplicity formulas for large discrete series, which are our main results. The multiplicity formulas are applied to a study on numbers of cuspidal automorphic representations of . [Copyright &y& Elsevier]