KOECHER-MAASS SERIES OF A CERTAIN HALF-INTEGRAL WEIGHT MODULAR FORM RELATED TO THE DUKE-IMAMOGLU-IKEDA LIFT

• Katsurada Hidenori

• Kawamura Hisa-aki

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-Imamo¯glu-Ikeda lift of h to the space of cusp forms of weight k for Spn(Z). Moreover, let φIn(h),1 be the first Fourier-Jacobi coefficient of In(h) and σn−1(φIn(h),1) be the cusp form in the generalized Kohnen plus space of weight k¡1/2 corresponding to φIn(h),1 under the Ibukiyama isomorphism. We then give an explicit formula for the Koecher-Maass series L(s, σn−1(φIn(h),1)) of σn−1(φIn(h),1) expressed in terms of the usual L-functions of h and f.

Journal

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 1038 1-41, 2013-06-28

  Department of Mathematics, Hokkaido University

Keywords

• Koecher-Maass series
• Duke-Imamoglu-Ikeda lift

Details

• CRID: 1390290699772183680
• NII Article ID: 120006459727
• DOI: 10.14943/84182
• HANDLE: 2115/69842
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • CiNii Articles
• Abstract License Flag: Allowed