Sums of squares in real quadratic fields and Hilbert modular groups

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.

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2020-02, Vol.52 (1), p.244-259
Main Authors: Chamizo, Fernando, Miatello, Roberto J.
Format: Article
Language:English
Subjects:
11F41
11F72 (primary)
11N45 (secondary)
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Description
Summary: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.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12323