2013/09/09 by Hidenori Katsurada, Katsurada, Hidenori, Hisa-aki Kawamura +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1309.2065
openalex publication_date 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in\nthe Kohnen plus space of weight k-n/2+1/2, let f be the corresponding primitive\nform of weight 2k-n for SL(2,Z) under the Shimura correspondence, and I(h) the\nDuke-Imamoglu-Ikeda lift of h to the space of cusp forms of weight k of genus\nn. Moreover, let FJ(I(h),1) be the first Fourier-Jacobi coefficient of I(h) and\ns(FJ(I(h),1)) be the cusp form in the generalized Kohnen plus space of weight\nk-1/2 corresponding to FJ(I(h),1) under the Ibukiyama isomorphism. We then give\nan explicit formula for the Koecher-Maass series of s(FJ(I(h),1)) expressed in\nterms of the usual L-functions of h and f.\n