본문 바로가기
KERD
논문KCI 등재

The cusp structure of the paramodular groups for degree two

3

조회

0

다운로드

2

인용

0

참고문헌

키워드

주제분류수학

초록

We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.

Abstract

We describe the one-dimensional and zero-dimensional cusps of the Satake compactification for the paramodular groups in degree two for arbitrary levels. We determine the crossings of the one-dimensional cusps. Applications to computing the dimensions of Siegel modular forms are given.

참고문헌 (19)

  1. S. B¨ocherer, "Surjectivity of Siegel Φ-operator for square free level and small weight", Annales de l’institut Fourier, 62(1), pp.121~144 (2012)
  2. A. Brumer, "Paramodular abelian varieties of odd conductor", arXiv: 1004.4699, ~
  3. U. Christian, "Einf¨uhrung in die Theorie der paramodularen Gruppen", Math. Ann, 168, pp.59~104 (1967)
  4. F. Diamond, "A First Course in Modular Forms", pp.14~436 (2005), Springer-Verlag
  5. E. Freitag, "Siegelsche Modulfunktionen, Grundlehren der mathematischen Wissenschaften, Band 254" (1983), Springer-Verlag
  6. V. Gritsenko, "Irrationality of the moduli spaces of polarized abelian surfaces", Internat. Math. Res. Notices, 1994(6), pp.9~ (1994)
  7. V. Gritsenko, "Minimal Siegel modular threefolds", Math. Proc. Cambridge Philos. Soc, 123(3), pp.461~485 (1998)
  8. T. Ibukiyama, "On some alternating sum of dimensions of Siegel cusp forms of general degree and cusp configurations", J. Fac. Sci. Univ. Tokyo Sec. IA Math, 40(2), pp.245~283 (1993)
  9. T. Ibukiyama, "Dimension formulas of Siegel modular forms of weight 3 and supersingular abelian surfaces, Siegel Modular Forms and Abelian Varieties", Proceedings of the 4-th Spring Conference on Modular Forms and Related Topics, pp.39~60 (2007)
  10. T. Ibukiyama, "On relations of dimensions of automorphic forms of Sp(2,R) and its compact twist Sp(2) (I), Automorphic forms and number theory", Adv. Stud. Pure Math., 7, pp.7~30 (1985), North-Holland
  11. T. Ibukiyama, "Dimensions of paramodular cusp forms for squarefree levels", ~
  12. T. Ibukiyama, "Jacobi forms that characterize paramodular forms", ~ (2011)
  13. J.-I. Igusa, "Theta Functions, Die Grundlehren der mathematischen Wissenschaften, Band 194" (1972), Springer-Verlag
  14. H. Reefschl¨ager, "Berechnung der Anzahl der 1-Spitzen der Paramodularen Gruppen 2- ten Grades", pp.1973
  15. B. Roberts, "Local Newforms for GSp(4)", Springer Lecture Note in Mathematics, 1918 (2007), Springer-Verlag
  16. I. Satake, "Compactification de espaces quotients de Siegel II", S´eminaire Cartan,, pp.1~10 (1957), E. N. S.
  17. I. Satake, "L’op´erateur Φ", S´eminaire Cartan, pp.1~18 (1957), E. N. S
  18. I. Satake, "Surjectivit´e globale de op´erateur Φ", S´eminaire Cartan, pp.1~17 (1957), E. N. S
  19. C. Siegel, "Moduln Abelscher Funktionen, Nachrichten der Akademie der Wissenschaften in G¨ottingen", Mathematisch-physikalische Klasse, 25, pp.365~427 (1960)

관련 논문AI추천

이 간행물의 다른 논문 (11건)