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Dirichlet series in the theory of Siegel modular forms

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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We are concerned with Dirichlet series which appear in the Fourier expansion of the non-analytic Eisenstein series on the Siegel upper half space Hm of degree m. In the case of m = 2 Kaufhold [1] evaluated them. Here we treat the general cases by a different method.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Kaufhold, G., Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades, Math. Ann., 137 (1959), 454476.Google Scholar
[ 2 ] Kitaoka, Y., Modular forms of degree n and representation by quadratic forms II, Nagoya Math. J., 87 (1982), 127146.CrossRefGoogle Scholar
[ 3 ] Kitaoka, Y., A note on local densities of quadratic forms, Nagoya Math. J., 92 (1983), 145152.CrossRefGoogle Scholar
[ 4 ] Maaβ, H., Die Fourierkoeffizienten der Eisensteinreihen zweiten Grades, Mat.-Fys. Medd. Danske Vid. Selsk., 34 (1964), no. 7.Google Scholar
[ 5 ] Maafi, H., Siegel’s modular forms and Dirichlet series, Lecture Notes in Mathematics, vol. 216. Berlin, Heidelberg, New York, Springer 1971.Google Scholar
[ 6 ] Shimura, G., Confluent hyper geometric functions on tube domains, Math. Ann., 260 (1982), 269302.CrossRefGoogle Scholar
[ 7 ] Shimura, G., On Eisenstein series, to appear in Duke Math. J.Google Scholar
[ 8 ] Siegel, C.L., Über die analytische Theorie der quadratischen Formen, Ann. of Math., 36 (1935), 527606.Google Scholar