On Gauss sum characters of finite groups and generalized Bernoulli numbers

Shoichi Nakajima

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 1, page 143-154
  • ISSN: 1246-7405

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Nakajima, Shoichi. "On Gauss sum characters of finite groups and generalized Bernoulli numbers." Journal de théorie des nombres de Bordeaux 7.1 (1995): 143-154. <http://eudml.org/doc/247651>.

@article{Nakajima1995,
author = {Nakajima, Shoichi},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Galois covering; compact Riemann surfaces; holomorphic differentials; Gauss sum characters; generalized Bernoulli number},
language = {eng},
number = {1},
pages = {143-154},
publisher = {Université Bordeaux I},
title = {On Gauss sum characters of finite groups and generalized Bernoulli numbers},
url = {http://eudml.org/doc/247651},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Nakajima, Shoichi
TI - On Gauss sum characters of finite groups and generalized Bernoulli numbers
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 143
EP - 154
LA - eng
KW - Galois covering; compact Riemann surfaces; holomorphic differentials; Gauss sum characters; generalized Bernoulli number
UR - http://eudml.org/doc/247651
ER -

References

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  2. [2] H. Feldmann, Über das Verhalten der Modulfunktionen von Primzahlstufe bei beliebigen Modulsubstitutionen, Abh. Math. Sem. Hamburg Univ.8 (1931), 323-347. Zbl0002.19804JFM57.0445.01
  3. [3] R. Hartshorne, Algebraic Geometry, Springer Verlag, New York-Heidelberg -Berlin, 1977. Zbl0367.14001MR463157
  4. [4] K. Hashimoto, Representations of the finite symplectic group Sp(4, Fp) in the spaces of Siegel modular forms, Contemporary Math.53 (1986), 253-276. Zbl0592.10024
  5. [5] H. Hasse, Vorlesungen über Zahlentheorie, zweite Auflage, Springer Verlag, Berlin-Gottingen- Heidelberg-New York, 1964. MR188128
  6. [6] E. Hecke, Mathematische Werke, zweite Auflage, Vandenhoeck & Ruprecht, Göttingen, 1970. Zbl0205.28902MR371577
  7. [7] H. Joris, On the evaluation of Gaussian sums for non-primitive Dirichlet characters, L'enseignement math.23 (1977), 13-18. Zbl0352.10018MR441888
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  10. [10] S. Nakajima, Action of finite groups on the holomorphic differentials of Riemann surfaces and the class numbers of imaginary quadratic fields, Reports of Number Theory Symposium, Osaka in Japanese (1989), 37-42. 
  11. [11] H. Saito, On the representation of SL2 (Fq) in the space of Hilbert modular forms, J. Math. Kyoto Univ.15 (1975), 101-128. Zbl0305.10022MR384706
  12. [12] J.-P. Serre, Linear Representations of Finite Groups, Springer Verlag, BerlinHeidelberg- New York, 1977. Zbl0355.20006MR450380
  13. [13] K. Shih, On the construction of Galois extensions of function fields and number fields, Math. Ann.207 (1974), 99-120. Zbl0279.12102MR332725
  14. [14] H. Spies, Die Darstellung der inhomogenen Modulargruppe mod qn durch die ganzen Modulformen gerader Dimension, Math. Ann.111 (1935), 329-354. Zbl0012.10101MR1512999JFM61.0110.03
  15. [15] L.C. Washington, Introduction to cyclotomic fields, Springer Verlag, New York-Heidelberg -Berlin, 1982. Zbl0484.12001MR718674
  16. [16] A. Weil, Über Matrizenringe auf Riemannschen flächen und den Riemann-Rochschen Satz, Abh. Math. Sem. Hamburg Univ.11 (1935), 110-115, A. Weil: Collected Papers, I,80-85. Zbl0011.12203JFM61.0123.01
  17. [17] S.H. Weintraub, PSL2(Zp) and the Atiyah-Bott fixed-point theorem, Houston J. Math.6 (1980), 427-430. ' Zbl0463.10016MR597780

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