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p-Adic properties of Siegel modular forms of degree 2

Published online by Cambridge University Press:  22 January 2016

Shōyū Nagaoka*
Affiliation:
Department of Mathematics, Hokkaido University
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H. P. F. Swinnerton-Dyer determined the structure of the algebra of modular forms mod p for all prime numbers p in elliptic modular case (cf. [10]). Using his result, J.-P. Serre investigated the properties of p-adic modular forms and succeeded to construct the p-adic zeta functions for any totally real number fields (cf. [8]).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Borevich, Z. I. and Shafarevich, I. R., Number Theory, Academic Press.Google Scholar
[2] Freitag, E., Zur Theorie der Modulformen zweiten Grades, Nach. Acad. Wiss. Gottingen II, 1965.Google Scholar
[3] Igusa, J., On Siegel modular forms of genus two (I), Amer. J. Math., 84, 1962.Google Scholar
[4] Igusa, J., On Siegel modular forms of genus two (II), Amer. J. Math., 86, 1964.Google Scholar
[5] Johnson, W., Irregular primes and cyclotomic Invariants, Math, of Computation, 29, 129, 1975.CrossRefGoogle Scholar
[6] Maass, H., Die Fourierkoeffizienten der Eisensteinreihen zweiten Grades, Mat-Fys. Medd. Danske Vid. Selsk., 34, 1964.Google Scholar
[7] Serre, J.-P., Congruences et formes modulaires, Sem. Bourbaki., 416, 1971/1972.Google Scholar
[8] Serre, J.-P., Formes modulaires et fonctions zêta p-adiques, Lecture Note in Math., 350, Springer Verlag, 1972.Google Scholar
[9] Siegel, C.L., Über die Fourierschen Koeffizienten der Eisensteinschen Reihen, Mat-Fys. Medd. Danske Vid. Selsk., 34, 1964.Google Scholar
[10] Swinnerton-Dyer, H. P. F., On Z-adic representations and congruences for coefficients of modular forms, Lecture Note in Math., 350, Springer Verlag, 1972.Google Scholar
[11] Witt, E., Ein Identitat zwischen Modulformen zweiten Grades, Abh. Math. Sem. Hansische Universitat., 14, 1941.Google Scholar