Congruence properties of Hermitian modular forms
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- by Toshiyuki Kikuta and Shoyu Nagaoka
- Proc. Amer. Math. Soc. 137 (2009), 1179-1184
- DOI: https://doi.org/10.1090/S0002-9939-08-09646-9
- Published electronically: September 25, 2008
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Abstract:
We study the existence of a modular form satisfying a certain congruence relation. The existence of such modular forms plays an important role in the determination of the structure of a ring of modular forms modulo $p$. We give a criterion for the existence of such a modular form in the case of Hermitian modular forms.References
- Eva Bayer-Fluckiger, Definite unimodular lattices having an automorphism of given characteristic polynomial, Comment. Math. Helv. 59 (1984), no. 4, 509–538. MR 780074, DOI 10.1007/BF02566364
- Siegfried Böcherer and Shoyu Nagaoka, On mod $p$ properties of Siegel modular forms, Math. Ann. 338 (2007), no. 2, 421–433. MR 2302069, DOI 10.1007/s00208-007-0081-7
- Hel Braun, Hermitian modular functions, Ann. of Math. (2) 50 (1949), 827–855. MR 32699, DOI 10.2307/1969581
- David Mordecai Cohen and H. L. Resnikoff, Hermitian quadratic forms and Hermitian modular forms, Pacific J. Math. 76 (1978), no. 2, 329–337. MR 506135, DOI 10.2140/pjm.1978.76.329
- Eberhard Freitag, Modulformen zweiten Grades zum rationalen und Gaußschen Zahlkörper, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1967 (1967), 3–49 (German). MR 0214541
- Jean-Pierre Serre, Formes modulaires et fonctions zêta $p$-adiques, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973, pp. 191–268 (French). MR 0404145
- H. P. F. Swinnerton-Dyer, On $l$-adic representations and congruences for coefficients of modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 350, Springer, Berlin, 1973, pp. 1–55. MR 0406931
Bibliographic Information
- Toshiyuki Kikuta
- Affiliation: Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
- Email: kikuta@math.kindai.ac.jp
- Shoyu Nagaoka
- Affiliation: Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
- Email: nagaoka@math.kindai.ac.jp
- Received by editor(s): April 1, 2008
- Published electronically: September 25, 2008
- Additional Notes: The second author was supported in part by Grant-in-Aid for Scientific Research 19540061.
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1179-1184
- MSC (2000): Primary 11F33; Secondary 11F55
- DOI: https://doi.org/10.1090/S0002-9939-08-09646-9
- MathSciNet review: 2465638
Dedicated: In celebration of Tomoyoshi Ibukiyama’s 60th birthday