On effective determination of symmetric-square lifts

Qingfeng Sun

Open Mathematics (2014)

  • Volume: 12, Issue: 7, page 976-990
  • ISSN: 2391-5455

Abstract

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Let F be the symmetric-square lift with Laplace eigenvalue λ F (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.

How to cite

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Qingfeng Sun. "On effective determination of symmetric-square lifts." Open Mathematics 12.7 (2014): 976-990. <http://eudml.org/doc/269699>.

@article{QingfengSun2014,
abstract = {Let F be the symmetric-square lift with Laplace eigenvalue λ F (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max \{4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)\} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.},
author = {Qingfeng Sun},
journal = {Open Mathematics},
keywords = {Symmetric-square lift; Effective determination; Rankin-Selberg L-function; symmetric-square lift; effective determination; Rankin-Selberg -function},
language = {eng},
number = {7},
pages = {976-990},
title = {On effective determination of symmetric-square lifts},
url = {http://eudml.org/doc/269699},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Qingfeng Sun
TI - On effective determination of symmetric-square lifts
JO - Open Mathematics
PY - 2014
VL - 12
IS - 7
SP - 976
EP - 990
AB - Let F be the symmetric-square lift with Laplace eigenvalue λ F (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.
LA - eng
KW - Symmetric-square lift; Effective determination; Rankin-Selberg L-function; symmetric-square lift; effective determination; Rankin-Selberg -function
UR - http://eudml.org/doc/269699
ER -

References

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