본문 바로가기
KERD
논문KCI 등재

Theta sums of higher index

2

조회

0

다운로드

1

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we obtain some behaviours of theta sums of higher index for the Schr{\"o}dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree $m$.

Abstract

In this paper, we obtain some behaviours of theta sums of higher index for the Schr{\"o}dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree $m$.

참고문헌 (29)

  1. R. Berndt, "Elements of theRepresentation Theory of the Jacobi Group" (1998), Birkhauser
  2. M. Eichler, "The Theory of Jacobi Forms" (1985), Birkh¨auser
  3. E. Freitag, "Siegelsche Modulfunktionen" (1983), Springer-Verlag
  4. M. Itoh, "Invariant Differential Operators on the Siegel-Jacobi Space", submitted, ~ (2015)
  5. G. Lion, "The Weil representation, Maslov index and Theta seires" (1980), Birkhauser
  6. J. Marklof, "Pair correlation densities of inhomogeneous quadratic forms", Ann. of Math, 158(2), pp.419~471 (2003)
  7. D. Mumford, "Tata Lectures on Theta I" (1983)
  8. A. Pitale, "Jacobi Maass forms", Abh. Math. Semin. Univ. Hambg, 79(1), pp.87~111 (2009)
  9. C. L. Siegel, "Gesammelte Abhandlungen, Band III", pp.105~142 (1966), Springer-Verlag
  10. A. Weil, "Collected Papers (1964-1978), Vol. III", pp.1~69 (1979), Springer-Verlag
  11. J.-H. Yang, "Harmonic analysis on the quotient spaces of Heisenberg groups", Nagoya Math. J, 123, pp.103~117 (1991)
  12. J.-H. Yang, "The Siegel-Jacobi operator", Abh. Math. Sem. Univ. Hamburg, 63, pp.135~146 (1993)
  13. J.-H. Yang, "Remarks on Jacobi forms of higher degree", Proc. of the 1993 Workshop on Automorphic Forms and Related Topics, pp.33~58 (1993), Pyungsan Institute for Mathematical Sciences
  14. J.-H. Yang, "Harmonic analysis on the quotient Spaces of Heisenberg groups II", J. Number Theory, 49(1), pp.63~72 (1994)
  15. J.-H. Yang, "Singular Jacobi forms", Trans. Amer. Math. Soc, 347(6), pp.2041~2049 (1995)
  16. J.-H. Yang, "Construction of vector valued modular forms from Jacobi forms", Canad. J. Math, 47(6), pp.1329~1339 (1995)
  17. J.-H. Yang, "A decomposition theorem on differential polynomials of theta functions of high level", Japa. J. Math, 22(1), pp.37~49 (1996)
  18. J.-H. Yang, "Fock representations of the Heisenberg group H (g,h)R", J. Korean Math. Soc, 34(2), pp.345~370 (1997)
  19. J.-H. Yang, "Lattice representations of Heisenberg groups", Math. Ann, 317(2), pp.309~323 (2000)
  20. J.-H. Yang, "A note on a fundamental domain for Siegel-Jacobi space", Houston J. Math, 32(3), pp.701~712 (2006)
  21. J.-H. Yang, "Invariant metrics and Laplacians on Siegel-Jacobi space", J. Number Theory, 127(1), pp.83~102 (2007)
  22. 양재현, "A Partial Cayley Transform of Siegel-Jacobi Disk", 대한수학회지, 45(3), pp.781~794 (2008), 대한수학회
  23. J.-H. Yang, "Invariant metrics and Laplacians on Siegel-Jacobi disk", Chinese Ann. Math, 31B(1), pp.85~100 (2010)
  24. J.-H. Yang, "Theta Functions and the Weil Representation" (2012), Kyung Moon Sa
  25. 양재현, "A Note on Maass-Jacobi Forms II", Kyungpook Mathematical Journal, 53(1), pp.49~86 (2013), 경북대학교 자연과학대학 수학과
  26. J.-H. Yang, "Geometry and arithmetic on the Siegel-Jacobi space, Geometry and Analysis on Manifolds, In Memory of Professor Shoshichi Kobayashi", Progress in Mathematics, 308, pp.275~325 (2015), Springer International Publishing AG Switzerland
  27. 양재현, "COVARIANT MAPS FOR THE SCHR¨ODINGER-WEIL REPRESENTATION", 대한수학회보, 52(2), pp.627~647 (2015), 대한수학회
  28. 양재현, "Sectional curvatures of the Siegel-Jacobi space", 대한수학회보, 50(3), pp.787~799 (2013), 대한수학회
  29. C. Ziegler, "Jacobi forms of higher degree", Abh. Math. Semin. Univ. Hambg, 59, pp.191~224 (1989)

관련 논문AI추천

이 간행물의 다른 논문 (27건)