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 Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 174–194 (Mi msb1992)

Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties

V. G. Zhuravlev

Abstract: Using the method of A. N. Andrianov, we establish a connection between the Fourier coefficients of Siegel modular forms $F$ of half-integral weight and the eigenvalues of operators in the local Hecke rings $\mathbf L_p^n(\varkappa)$ for the symplectic covering group $\mathrm{GSp}_n^+(\mathbf R)$ of degree $n$. These results are used for analytic continuation of the standard zeta-functions associated to $F$.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 169–190

Bibliographic databases:

UDC: 511
MSC: Primary 10D20, 10D24; Secondary 10H10, 12A70, 32N05

Citation: V. G. Zhuravlev, “Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties”, Mat. Sb. (N.S.), 123(165):2 (1984), 174–194; Math. USSR-Sb., 51:1 (1985), 169–190

Citation in format AMSBIB
\Bibitem{Zhu84} \by V.~G.~Zhuravlev \paper Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties \jour Mat. Sb. (N.S.) \yr 1984 \vol 123(165) \issue 2 \pages 174--194 \mathnet{http://mi.mathnet.ru/msb1992} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=732384} \zmath{https://zbmath.org/?q=an:0571.10029|0537.10017} \transl \jour Math. USSR-Sb. \yr 1985 \vol 51 \issue 1 \pages 169--190 \crossref{https://doi.org/10.1070/SM1985v051n01ABEH002853} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. G. Zhuravlev, “Explicit duality formulas for symplectic and orthogonal Hecke operators on theta-series of positive quadratic forms”, Math. USSR-Sb., 58:2 (1987), 417–434
2. A. N. Andrianov, “The action of Hecke operators on nonhomogeneous theta series”, Math. USSR-Sb., 59:2 (1988), 269–285
3. Bump D. Furusawa M. Ginzburg D., “Non-Unique Models in the Rankin-Selberg Method”, J. Reine Angew. Math., 468 (1995), 77–111
4. Hayashida S., “Zeta Function and Zharkovskaya's Theorem on Siegel Modular Forms of Half-Integral Weight”, Acta Arith., 108:4 (2003), 391–399
5. 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
6. Hayashida S. Ibukiyama T., “Siegel Modular Forms of Half Integral Weight and a Lifting Conjecture”, J. Math. Kyoto Univ., 45:3 (2005), 489–530
7. Ibukiyama T., “Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type”, Conference on l-Functions, eds. Weng L., Kaneko M., World Scientific Publ Co Pte Ltd, 2007, 55–69
8. 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
9. Hidenori Katsurada, Hisa-aki Kawamura, “Ikeda's conjecture on the period of the Duke–Imamoḡlu–Ikeda lift”, Proc. London Math. Soc, 2015, pdv011
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