Counting Automorphic Forms on Norm One Tori

TL;DR

This paper derives an asymptotic formula for counting automorphic forms on a specific type of algebraic torus related to imaginary quadratic fields, ordered by their analytic conductor.

Contribution

It provides the first asymptotic count of automorphic forms on non-split norm one tori associated with imaginary quadratic extensions.

Findings

Asymptotic formula for automorphic forms count

Ordered by analytic conductor

Applicable to non-split norm one tori

Abstract

We give an asymptotic formula for the number of automorphic forms on the non-split norm one torus $T$ associated with an imaginary quadratic extension of $\mathbb{Q}$, ordered by analytic conductor.