On the representation of integers by indefinite binary Hermitian forms

2010/04/19 by Jouni Parkkonen, Parkkonen, Jouni, Frédéric Paulin +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1004.3211

9 pages

arxiv created 2010/04/19 · openalex publication_date 2010/04/19 · arxiv updated 2010/04/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.

Citations

• Arithmetic Subgroups of Algebraic Groups

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• Farey neighbours, modular symbols and divergent geodesics

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