Weyl's law for the cuspidal spectrum of SL(n)

الأصل · EN

Let Γ be a principal congruence subgroup of SLₙ(Z) and let σ be an irreducible representation of SO(n). Let N(T,σ) be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for Γ which transform under SO(n) according to σ. We prove that the counting function N(T,σ) satisfies Weyl's law as T→∞. Especially this implies that there exist infinitely many cusp forms for the full modular group SLₙ(Z).