On the Petersson inner products of Fourier–Jacobi coefficients and Hecke eigenvalues of Siegel cusp forms

Kumar, Balesh; Paul, Biplab

doi:10.4064/aa190326-10-2

Cited by 2 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result has been generalized in arithmetic progression by Gun and Kumar [7] (see also [16] for recent progress in this direction). In the same article, Kohnen asked the possibility of…”

Section: Introductionmentioning

confidence: 75%

“…This result has been generalized in arithmetic progression by Gun and Kumar [7] (see also [16] for recent progress in this direction). In the same article, Kohnen asked the possibility of

\underset{m \to \infty}{lim sup} \frac{⟨ ϕ_{m}, ϕ_{m} ⟩}{m^{k - 1}} = \infty .

In the case when

n = 1

, this has been shown to be true by Rankin [19, Theorem 5] (further progress in this direction can be found in [1, 3, 18] and references there).…”

Section: Introductionmentioning

confidence: 90%

“…(b). Note that the bound

false| false⟨ ϕ_{m}, ψ_{m} false⟩ false| ≪_{F, G} m^{k - 1}

on average is optimal when

⟨ F, G ⟩ \neq 0

(see [16, Theorem 6]). But it seems to be far from being optimal when

⟨ F, G ⟩ = 0

.…”

Section: Ramanujan–petersson Conjecture On Averagementioning

confidence: 99%

See 2 more Smart Citations

Ramanujan–Petersson conjecture for Fourier–Jacobi coefficients of Siegel cusp forms

Kumar

Paul

2020

Bull. London Math. Soc.

Self Cite

View full text Add to dashboard Cite

Let F be a Siegel cusp form of weight k and degree n>1 with Fourier‐Jacobi coefficients {ϕm}m∈N. In this article, we investigate the Ramanujan–Petersson conjecture (formulated by Kohnen) for the Petersson norm of ϕm. 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 ϕm 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.

show abstract

“…This result has been generalized in arithmetic progression by Gun and Kumar [7] (see also [16] for recent progress in this direction). In the same article, Kohnen asked the possibility of…”

Section: Introductionmentioning

confidence: 75%

“…This result has been generalized in arithmetic progression by Gun and Kumar [7] (see also [16] for recent progress in this direction). In the same article, Kohnen asked the possibility of