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On the secondL-functions attached to Hilbert modular forms

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References

  1. Cohen, H.: Sums involving the values at negative integers ofL functions of quadratic characters. Math. Ann.217, 271–285 (1975)

    Google Scholar 

  2. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher transcendental functions, Vol. 1. New York, Toronto, London: McGraw-Hill 1953

    Google Scholar 

  3. Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Tables of integral transforms, Vol. 1. New York, Toronto, London: McGraw-Hill 1954

    Google Scholar 

  4. Furusawa, M.: On Petersson norms for some fiftings. Math. Ann.267, 543–548 (1984)

    Google Scholar 

  5. Gelbart, S., Jacquet, H.: A relation between automorphic representations of GL(2) and GL(3). Ann. scient. Ec. Norm. Sup.11, 471–542 (1978)

    Google Scholar 

  6. Gundlach, K.-B.: Über dic Darstellung der ganzen Spitzenformen zu den Idealstufen der Hilbertschen Modulgruppe und die Abschätzung ihrer Fourierkoeffizienten. Acta math.92, 309–345 (1954)

    Google Scholar 

  7. Gundlach, K.-B.: Poincarésche und Eisensteinsche Reihen zur Hilbertschen Modulgruppe. Math. Z.64, 339–352 (1956)

    Google Scholar 

  8. Hilbert, D.: Über die Theorie des relativquadratischen Zahlkörpers. Math. Ann.51, 1–127 (1899)

    Google Scholar 

  9. Klingen, H.: Über die Werte der Dedekindschen Zetafunktionen. Math. Ann.145, 265–272 (1962)

    Google Scholar 

  10. Kurokawa, N.: Congruences between Stegel modular forms of degree two. Proc. Japan Acad.55A, 417–422 (1979); II.57A, 140–145 (1981)

    Google Scholar 

  11. Maaß, H.: Zur Theorie der automorphen Funktionen vonn Veränderlichen. Math. Ann.117, 538–578 (1940)

    Google Scholar 

  12. Mizumoto, S.: Fourier coefficients of generalized Eisenstein series of degree two. I. Invent. Math.65, 115–135 (1981); II. Kodai Math. J.7, 86–110 (1984)

    Google Scholar 

  13. Mizumoto, S.: On Eisenstein series of degree two for Hilbert-Siegel modular groups. Proc. Janpan Acad.58A, 33–36 (1982)

    Google Scholar 

  14. Mizumoto, S.: On integrality of certain algebraic numbers associated with modular forms. Math. Ann.265, 119–135 (1983)

    Google Scholar 

  15. Shimizu, H.: On discontinuous groups operating on the product of the upper half planes. Ann. of Math.77, 33–71 (1963)

    Google Scholar 

  16. Shimura, G.: On the holomorphy of certain Dirichlet series. Proc. London Math. Soc.31, 79–98 (1975)

    Google Scholar 

  17. Shimura, G.: The special values of the zeta functions associated with Hilbert modular forms. Duke Math. J.45, 637–679 (1978)

    Google Scholar 

  18. Shintani, T.: On evaluation of zeta functions of totally real algebraic number fields at nonpositive integers. J. Fac. Sci. Univ. Tokyo23, 393–417 (1976)

    Google Scholar 

  19. Siegel, C.L.: Über die analytische Theorie der quadratischen Formen. III. Ann. of Math.38, 213–292 (1937)

    Google Scholar 

  20. Siegel, C.L.: Berechnung von Zetafunktionen an ganzzahligen Stellen. Nachr. Akad. Wiss. Göttingen10, 87–102 (1969)

    Google Scholar 

  21. Sturm, J.: Special values of zeta functions and Eisenstein series of half integral weight. Am. J. Math.102, 219–240 (1980)

    Google Scholar 

  22. Takase, K.: On special values of the secondL-functions attached to Hilbert modular forms (preprint)

  23. Zagier, D.: Modular forms whose Fourier coefficients involve zcta-functions of quadratic fields. Lecture Notes in Mathematics, Vol. 627, pp. 105–169, Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

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  1. Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, 152, Tokyo, Japan

    Shin-ichiro Mizumoto

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  1. Shin-ichiro Mizumoto
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Mizumoto, Si. On the secondL-functions attached to Hilbert modular forms. Math. Ann. 269, 191–216 (1984). https://doi.org/10.1007/BF01451419

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