On the Fourier coefficients of automorphic forms at various cusps and some applications to Rankin's convolution

Tetsuya ASAI

doi:10.2969/jmsj/02810048

Tetsuya ASAI

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ジャーナルフリー

1976 年 28 巻 1 号 p. 48-61

DOI https://doi.org/10.2969/jmsj/02810048

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Published: 1976 Received: 1974/09/03 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Tikao Tatuzawa on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. N. Andrianov, Dirichlet series with Euler product in the theory of Siegel modular forms of genus 2, Proc. Steklov Inst. Math., 112 (1971), 70-93.
2) A. O. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
3) K. Doi and H. Naganuma, On the functional equation of certain Dirichlet series, Invent, math., 9 (1969), 1-14.
4) E. Hecke, Mathematische Werke, Vandenhoech und Ruprecht.
5) H. Jacquet, Automorphic forms on GL(2), II, Lecture notes in math., 278, Springer, 1972.
6) Y. Kitaoka, On the transformation formula of theta-series, to appear.
7) T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann, of Math., 94 (1971), 174-189.
8) H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's Neben-type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Japan, 25 (1973), 547-555.
9) A. P. Ogg, On the eigenvalues of Hecke operators, Math. Ann., 179 (1969), 101-108.
10) A. P. Ogg, On a convolution of L-series, Invent. Math., 7 (1969), 297-312.
11) R. A. Rankin, Contribution to the theory of Ramanujan's function τ(n) and similar arithmetical functions, I, II, Proc. Cambridge Philos. Soc., 35 (1939), 351-372.
12) G. Shimura, Introduction to the arithmetical theory of automorphic functions, Publ. Math. Soc. Japan, No. 11.
13) G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
14) G. Shimura, On the holomorphy of certain Dirichlet series, to appear.

Right : [1] A. N. Andrianov, Dirichlet series with Euler product in the theory of Siegel modular forms of genus 2, Proc. Steklov Inst. Math., 112 (1971), 70-93.
[2] A. O. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann., 185 (1970), 134-160.
[3] K. Doi and H. Naganuma, On the functional equation of certain Dirichlet series, Invent. math., 9 (1969), 1-14.
[4] E. Hecke, Mathematische Werke, Vandenhoech und Ruprecht.
[5] H. Jacquet, Automorphic forms on GL (2), II, Lecture notes in math., 278, Springer, 1972.
[6] Y. Kitaoka, On the transformation formula of theta-series, to appear.
[7] T. Miyake, On automorphic forms on GL₂ and Hecke operators, Ann, of Math., 94 (1971), 174-189.
[8] H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's Neben-type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Japan, 25 (1973), 547-555.
[9] A. P. Ogg, On the eigenvalues of Hecke operators, Math. Ann., 179 (1969), 101-108.
[10] A. P. Ogg, On a convolution of L-series, Invent. Math., 7 (1969), 297-312.
[11] R. A. Rankin, Contribution to the theory of Ramanujan's function τ(n) and similar arithmetical functions, I, II, Proc. Cambridge Philos. Soc., 35 (1939), 351-372.
[12] G. Shimura, Introduction to the arithmetical theory of automorphic functions, Publ. Math. Soc. Japan, No. 11.
[13] G. Shimura, On modular forms of half integral weight, Ann. of Math., 97 (1973), 440-481.
[14] G. Shimura, On the holomorphy of certain Dirichlet series, to appear.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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