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Estimates for Fourier coefficients of Hermitian cusp forms of degree two

Volume 183 / 2018

Arvind Kumar, B. Ramakrishnan Acta Arithmetica 183 (2018), 257-275 MSC: Primary 11F55; Secondary 11F50, 11F30. DOI: 10.4064/aa170301-26-10 Published online: 9 March 2018

Abstract

We determine the Fourier series development of Hermitian Jacobi Poincaré series and obtain bounds for its Fourier coefficients. This gives rise to estimates for Fourier coefficients of Hermitian Jacobi cusp forms in general. Then, by following the method of Kohnen (1993), we obtain estimates for Fourier coefficients of Hermitian cusp forms of degree two with respect to ${\mathbb Q}(i)$.

Authors

  • Arvind KumarHarish-Chandra Research Institute
    HBNI
    Chhatnag Road
    Jhunsi
    Allahabad 211019, India
    and
    School of Mathematical Sciences
    National Institute of Science Education and Research, Bhubaneswar
    HBNI
    Jatni, Khurda, Odisha 752 050, India
    e-mail
  • B. RamakrishnanHarish-Chandra Research Institute
    HBNI
    Chhatnag Road
    Jhunsi
    Allahabad 211019, India
    e-mail

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