Sums of squares in real quadratic fields and Hilbert modular groups

Abstract

We use the spectral theory of Hilbert–Maass forms for real quadratic fields to obtain the asymptotics of some sums involving the number of representations as a sum of two squares in the ring of integers.

Erratum

“…Between September 2019 and February 2020, twenty‐one research articles 1–21 were published in the Bulletin of the London Mathematical Society with incorrect copyright statements. The copyright in these articles is stated as belonging to the London Mathematical Society; however, that is incorrect and the copyright remains with the authors of those articles.…”