The Weyl law for algebraic tori (Q6566414)

In the analytic theory of automorphic forms, it is a crucial task to obtain a number of irreducible cuspidal automorphic representations of a given algebraic group \(G\) over a global field \(k\). In such a task, the representations of \(G\) are ordered by a positive real-valued invariant called the analytic conductor. The analytic conductor is canonically defined by the means of the local Langlands conjecture, using a finite-dimensional algebraic representation \(r\) of the complex \(L\)-group of \(G\).\N\NIn the paper under the review, the author obtains an asymptotic evaluation for the number of automorphic characters in the case when \(G = T\), a torus over \(k\), and \(r\) is an arbitrary complex algebraic representation of its \(L\)-group.