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

• Autorzy: Hidenori Katsurada , Hisa-aki Kawamura
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F67: Special values of automorphic L -series, periods of modular forms, cohomology, modular symbols
• 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 1
• Strony: 1-42

Daty

wydano

2014

Twórcy

autor

Hidenori Katsurada

• Muroran Institute of Technology, Mizumoto 27-1, Muroran, 050-8585, Japan

autor

Hisa-aki Kawamura

• Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, 060-0810, Japan
• Department of Mathematics, Hiroshima University, 1-7-1 Kagamiyama, Higashi-Hiroshima, 739-8521, Japan

Identyfikatory

DOI

10.4064/aa162-1-1