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Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two

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References

  1. Andrianov, A.N.: Euler products corresponding to Siegel modular forms of genus 2. Russ. Math. Surv.29, 45–116 (1974) (Engl. transl.)

    Google Scholar 

  2. Baily, W.L.: Automorphic forms with integral Fourier coefficients. In: Lect. Notes Math. 155, pp. 1–8. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  3. Böcherer, S.: Über gewisse Siegelsche Modulformen zweiten Grades. Math. Ann.261, 23–41 (1982)

    Google Scholar 

  4. Eichler: Zur Begründung der Theorie der automorphen Funktionen in mehreren Variablen. Aequationes Math.3, 93–111 (1969)

    Google Scholar 

  5. Igusa, J.: On the ring of modular forms of degree two overZ. Am. J. Math.101, 149–183 (1979)

    Google Scholar 

  6. Klingen, H.: Zum Darstellungssatz für Siegelsche Modulformen. Math. Z.102, 30–43 (1967)

    Google Scholar 

  7. Kurokawa, N.: Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two. Invent. Math.49, 149–165 (1978)

    Article  Google Scholar 

  8. Kurokawa, N.: Congruences between Siegel modular forms of degree two. Proc. Japan Acad.55A, 417–422 (1979)

    Google Scholar 

  9. Kurokawa, N.: Congruences between Siegel modular forms of degree two. II. Proc. Japan Acad.57A, 140–145 (1981)

    Google Scholar 

  10. Kurokawa, N.: On Siegel eigenforms. Proc. Japan Acad.57A, 47–50 (1981)

    Google Scholar 

  11. Kurokawa, N.: On Eisenstein series for Siegel modular groups. Proc. Japan Acad.57A, 51–55 (1981)

    Google Scholar 

  12. Kurokawa, N.: On Eisenstein series for Siegel modular groups. II. Proc. Japan Acad.57A, 315–320 (1981)

    Google Scholar 

  13. Langlands, R.P.: On the functional equations satisfied by Eisenstein series. Lect. Notes Math. 544. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  14. Mizumoto, S.: Fourier coefficients of generalized Eisenstein series of degree two. I. Invent. Math.65, 115–135 (1981)

    Google Scholar 

  15. Mizumoto, S.: Fourier coefficients of generalized Eisenstein series of degree two. II. Kodai Math. J.7, 86–110 (1984)

    Google Scholar 

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

    Google Scholar 

  17. Mizumoto, S.: On the secondL-functions attached to Hilbert modular forms. Math. Ann.269, 191–216 (1984)

    Google Scholar 

  18. Ozeki, M.: A product formula for Fourier coefficients of Siegel modular forms. (Japanese manuscript.) Sûriken Kôkyûroku546, 110–125 (1985), RIMS, Univ. Kyoto

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  21. Wagstaff, S.S.: The irregular primes to 125000. Math. Comput.32, 583–591 (1978)

    Google Scholar 

  22. Zagier, D.: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields. In: Lect. Notes Math. 627, pp. 105–169. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

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Mizumoto, Si. Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two. Math. Ann. 275, 149–161 (1986). https://doi.org/10.1007/BF01458589

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  • DOI: https://doi.org/10.1007/BF01458589

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