Eisenstein series whose Fourier coefficients are zeta functions of binary Hermitian forms

2020/02/22 by Jorge Vargas Florez, Jorge Flórez, Cihan Karabulut +4
Mathematics · #11F30 #11M36 (primary) #32N10 (secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F30 #msc:11M36 #msc:32N10

paper · pdf · doi:10.48550/arxiv.2002.09819

Accepted for publication in the Proceedings of the American Mathematical Society. 10pp

openalex publication_date 2020/02/22 · arxiv created 2020/02/23 · arxiv updated 2020/02/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating series are Eisenstein series. As a consequence we obtain an explicit formula for the special values of zeta functions associated with binary Hermitian forms.

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