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Koecher-Maass series に関する文献表

Koecher Maass 級数に関する文献表をまとめておいた方が何かと便利であろうとの提案

を受けて、本文の著者に提案していただき直接関係がありそうなものを以下にまとめまし た。従ってたとえばアイゼンシュタイン級数のフーリエ係数のみについて述べた文献は重 要な文献であっても省略しました。また、2次形式のゼータ関数はKoecher Maass級数の 1種ではありますが、これまで含めると文献が多岐にわたりすぎると考え、ほとんど省略 しました。(Siegel 全集その他をみてください。)報告集で引用された文献とは多少相補的 な関係にありますが、時間的な制約から、完全を期したものにはなっていない点、ご容赦 願います。

References

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[3] T. Arakawa, Dirichlet series corresponding to Siegel’s modular forms of degree n with level N. Tohoku Math. J. (2)42(1990), no.2, 261-286.

[4] T. Arakawa, Koecher-Maass series corresponding to Jacobi forms and Cohen Eisen- stein series, Comment. Math. Univ. St. Pauli 47(1998), 93–122.

[5] S. B¨ocherer, Bemerkungen ¨uber die Dirichletreihen von Koecher und Maass, Math- ematica Gottingensis Schriftreihe des SFB, Geometrie und Analysis, Heft 68, 1986.

[6] S. B¨ocherer and R. Schulze-Pillot, On a theorem of Waldspurger and on Eisenstein series of Klingen type, Math. Ann., 288(1990), 361-388.

[7] S. B¨ocherer and R. Schulze-Pillot, The Dirichlet series of Koecher and Maass and modular forms of weight 3/2, Math. Z., 209(1992), 273-287.

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[8] S. B¨ocherer and R. Schulze-Pillot, Mellin transform of vector valued theta series attached to quaternion algebras.Math. Nach. 169(1994), 31–57.

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[14] T. Ibukiyama and H. Katsurada, An explicit form of Koecher-Maass series of Siegel Eisenstein series, preprint.

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[16] T. Ibukiyama and H. Katsurada, An explicit form of Koecher Maass Dirichlet series for Klingen’s Eisentein series, preprint.

[17] Y. Kitaoka, Representations of quadratic forms and their application to Selberg zeta functions, Nagoya Mathe.J. 63(1976)153-162

[18] M. Koecher, ¨Uber Dirichlet-Reihen mit Funktionalgleichung, J. reine Angew. Math.

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[19] A. Krieg, Koecher-Maass series for modular forms of quaternions, Manuscripta Math. 66(1990), no.4, 431–451.

[20] H. Klingen, Introductory lectures on Siegel modular forms, Cambridge University Press, 1990, Cambridge, New York, Port Chester, Melbourne, Sydney.

[21] H. Maass, Spherical functions and quadratic forms.J. Indian Math. Soc.20(1956), 117–162.

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[23] H. Maass, ¨Uber die r¨aumliche Verteilung der Punkte in Gittern mit indefiniter Metrik.Math. Ann. 138(1959), 287–315.

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