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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 263, Pages 105–140 (Mi znsl1138)  

On some metaplectic Eisenstein series

D. S. Kataev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract: We study cubic metaplectic Eisenstein series connected with the Jacobi maximal parabolic subgroup of a symplectic group. We use the so-called $sl(2)$-triples" technique in order to evaluate the Fourier coefficients of these series. In Secs. 1 and 2, we introduce the necessary notation and study the group $\Gamma(q)$ and its subgroups in detail. In Sec. 3, we prove the main result of the present paper (Theorem 1). Section 4 is devoted to the study of the Dirichlet series appearing in Theorem 1.
Received: 04.11.1999
English version:
Journal of Mathematical Sciences (New York), 2002, Volume 110, Issue 6, Pages 3091–3110
DOI: https://doi.org/10.1023/A:1015472328214
Bibliographic databases:
UDC: 517.3
Language: Russian
Citation: D. S. Kataev, “On some metaplectic Eisenstein series”, Analytical theory of numbers and theory of functions. Part 16, Zap. Nauchn. Sem. POMI, 263, POMI, St. Petersburg, 2000, 105–140; J. Math. Sci. (New York), 110:6 (2002), 3091–3110
Citation in format AMSBIB
\Bibitem{Kat00}
\by D.~S.~Kataev
\paper On some metaplectic Eisenstein series
\inbook Analytical theory of numbers and theory of functions. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 263
\pages 105--140
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1138}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1756342}
\zmath{https://zbmath.org/?q=an:1004.11022}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 110
\issue 6
\pages 3091--3110
\crossref{https://doi.org/10.1023/A:1015472328214}
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