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Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms
Author(s) -
Kumar Balesh,
Paul Biplab
Publication year - 2021
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12419
Subject(s) - mathematics , ramanujan's sum , cusp (singularity) , conjecture , pure mathematics , fourier series , cusp form , siegel modular form , algebra over a field , mathematical analysis , geometry , modular form
Let F be a Siegel cusp form of weight k and degree n > 1 with Fourier‐Jacobi coefficients{ ϕ m } m ∈ N . In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕ m . In particular, we show that this conjecture is true when F is a Hecke eigenform and a Duke–Imamoğlu–Ikeda lift. This generalizes a result of Kohnen and Sengupta. Further, we investigate an omega result and a lower bound for the Petersson norms of ϕ m as m → ∞ . Interestingly, these results are different depending on whether F is a Saito–Kurokawa lift or a Duke–Imamoğlu–Ikeda lift of degree n ⩾ 4 .