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 be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to under the Ibukiyama isomorphism. We give an explicit formula for the Koecher-Maass series of expressed in terms of the usual L-functions of h and f.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-1-1,
author = {Hidenori Katsurada and Hisa-aki Kawamura},
title = {Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamo\=glu-Ikeda lift},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {1-42},
zbl = {1322.11041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-1-1}
}
Hidenori Katsurada; Hisa-aki Kawamura. Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift. Acta Arithmetica, Tome 166 (2014) pp. 1-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa162-1-1/