Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift

Hidenori Katsurada, and Hisa-aki Kawamura. "Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift." Acta Arithmetica 162.1 (2014): 1-42. <http://eudml.org/doc/279613>.

@article{HidenoriKatsurada2014,
abstract = {Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let $ϕ_\{Iₙ(h),1\}$ be the first Fourier-Jacobi coefficient of Iₙ(h), and $σ_\{n-1\}(ϕ_\{Iₙ(h),1\})$ be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to $ϕ_\{Iₙ(h),1\}$ under the Ibukiyama isomorphism. We give an explicit formula for the Koecher-Maass series $L(s,σ_\{n-1\}(ϕ_\{Iₙ(h),1\}))$ of $σ_\{n-1\}(ϕ_\{Iₙ(h),1\})$ expressed in terms of the usual L-functions of h and f.},
author = {Hidenori Katsurada, Hisa-aki Kawamura},
journal = {Acta Arithmetica},
keywords = {Koecher-Maass series; half-integral weight modular form; Satake -parameter; Kohnen plus space},
language = {eng},
number = {1},
pages = {1-42},
title = {Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift},
url = {http://eudml.org/doc/279613},
volume = {162},
year = {2014},
}

TY - JOUR
AU - Hidenori Katsurada
AU - Hisa-aki Kawamura
TI - Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift
JO - Acta Arithmetica
PY - 2014
VL - 162
IS - 1
SP - 1
EP - 42
AB - Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let $ϕ_{Iₙ(h),1}$ be the first Fourier-Jacobi coefficient of Iₙ(h), and $σ_{n-1}(ϕ_{Iₙ(h),1})$ be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to $ϕ_{Iₙ(h),1}$ under the Ibukiyama isomorphism. We give an explicit formula for the Koecher-Maass series $L(s,σ_{n-1}(ϕ_{Iₙ(h),1}))$ of $σ_{n-1}(ϕ_{Iₙ(h),1})$ expressed in terms of the usual L-functions of h and f.
LA - eng
KW - Koecher-Maass series; half-integral weight modular form; Satake -parameter; Kohnen plus space
UR - http://eudml.org/doc/279613
ER -