Publicacions Matemàtiques

Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients

Pramath Anamby and Soumya Das

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Abstract

We prove that Hermitian cusp forms of weight $k$ for the Hermitian modular group of degree 2 are determined by their Fourier coefficients indexed by matrices whose determinants are essentially square-free. Moreover, we give a quantitative version of the above result. This is a consequence of the corresponding results for integral weight elliptic cusp forms, which are also treated in this paper.

Article information

Source
Publ. Mat., Volume 63, Number 1 (2019), 307-341.

Dates
Received: 3 July 2017
Revised: 25 July 2018
First available in Project Euclid: 7 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.pm/1544151640

Digital Object Identifier
doi:10.5565/PUBLMAT6311911

Mathematical Reviews number (MathSciNet)
MR3908796

Zentralblatt MATH identifier
07040971

Subjects
Primary: 11F30: Fourier coefficients of automorphic forms 11F55: Other groups and their modular and automorphic forms (several variables)
Secondary: 11F50: Jacobi forms

Keywords
Hermitian modular forms square free Fourier coefficients Hermitian Jacobi forms Eichler–Zagier maps

Citation

Anamby, Pramath; Das, Soumya. Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients. Publ. Mat. 63 (2019), no. 1, 307--341. doi:10.5565/PUBLMAT6311911. https://projecteuclid.org/euclid.pm/1544151640


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