Abstract:
Using the standard theta series of genus nn, the Hecke rings ˆD=ˆD(Γn0(q),Sn(q))^D=^D(Γn0(q),Sn(q)), for a covering G of the symplectic group GSp+n(R) are constructed. The special role of four subrings of ˆD is described, as well as some finitely generated arithmetic subrings ˆLnp(ϰ). The latter are important in the study of multiplicative properties of the Fourier coefficients of Siegel modular forms of half-integral weight.
Bibliography: 11 titles.
\Bibitem{Zhu83}
\by V.~G.~Zhuravlev
\paper Hecke rings for a~covering of the symplectic group
\jour Math. USSR-Sb.
\yr 1984
\vol 49
\issue 2
\pages 379--399
\mathnet{http://mi.mathnet.ru/eng/sm2208}
\crossref{https://doi.org/10.1070/SM1984v049n02ABEH002716}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=708003}
\zmath{https://zbmath.org/?q=an:0542.10021|0524.10021}
Linking options:
https://www.mathnet.ru/eng/sm2208
https://doi.org/10.1070/SM1984v049n02ABEH002716
https://www.mathnet.ru/eng/sm/v163/i3/p381
This publication is cited in the following 10 articles:
Salvatore Mercuri, “Algebraicity of metaplectic L-functions”, Journal of Number Theory, 219 (2021), 109
Lynne H. Walling, “A formula for the action of Hecke operators on half-integral weight Siegel modular forms and applications”, Journal of Number Theory, 133:5 (2013), 1608
Yamana Sh., “Determination of Holomorphic Modular Forms by Primitive Fourier Coefficients”, Math. Ann., 344:4 (2009), 853–862
Hayashida S., Ibukiyama T., “Siegel Modular Forms of Half Integral Weight and a Lifting Conjecture”, J. Math. Kyoto Univ., 45:3 (2005), 489–530
Hayashida S., “Skew-Holomorphic Jacobi Forms of Index 1 and Siegel Modular Forms of Half-Integral Weight”, J. Number Theory, 106:2 (2004), 200–218
Hayashida S., “Zeta Function and Zharkovskaya's Theorem on Siegel Modular Forms of Half-Integral Weight”, Acta Arith., 108:4 (2003), 391–399
K. Yokoi, “A certain relation between Jacobi forms of half integral weight and Siegel modular forms of integral weight”, Abh Math Semin Univ Hambg, 71:1 (2001), 91
Tomoyoshi Ibukiyama, Yasutaka Ihara, “On automorphic forms on the unitary symplectic group Sp(n) andSL 2(R)”, Math. Ann., 278:1-4 (1987), 307
A. N. Andrianov, “The action of Hecke operators on nonhomogeneous theta series”, Math. USSR-Sb., 59:2 (1988), 269–285
V. G. Zhuravlev, “Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties”, Math. USSR-Sb., 51:1 (1985), 169–190
Citation in format AMSBIB
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