Browse > Article
http://dx.doi.org/10.4134/BKMS.b160009

THETA SUMS OF HIGHER INDEX  

Yang, Jae-Hyun (Department of Mathematics Inha University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1893-1908 More about this Journal
Abstract
In this paper, we obtain some behaviours of theta sums of higher index for the $Schr{\ddot{o}}dinger$-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m.
Keywords
the $Schr{\ddot{o}}dinger$-Weil representation; theta sums;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 R. Berndt and R. Schmidt, Elements of theRepresentation Theory of the Jacobi Group, Birkhauser, 1998.
2 M. Eichler and D. Zagier, The Theory of Jacobi Forms, Progress in Math., 55, Birkhauser, Boston, Basel and Stuttgart, 1985.
3 E. Freitag, Siegelsche Modulfunktionen, Grundlehren de mathematischen Wissenschaften 55, Springer-Verlag, Berlin-Heidelberg-New York, 1983.
4 M. Itoh, H. Ochiai, and J.-H. Yang, Invariant Differential Operators on the Siegel-Jacobi Space, submitted, 2015.
5 G. Lion and M. Vergne, The Weil representation, Maslov index and Theta seires, Progress in Math., 6, Birkhauser, Boston, Basel and Stuttgart, 1980.
6 J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. 158 (2003), no. 2, 419-471.   DOI
7 D. Mumford, Tata Lectures on Theta I, Progress in Math. 28, Boston-Basel-Stuttgart, 1983.
8 J.-H. Yang, A partial Cayley transform of Siegel-Jacobi disk, J. Korean Math. Soc. 45 (2008), no. 3, 781-794.   DOI
9 J.-H. Yang, Invariant metrics and Laplacians on Siegel-Jacobi disk, Chinese Ann. Math. 31B (2010), no. 1, 85-100.
10 J.-H. Yang, Heisenberg Group, Theta Functions and the Weil Representation, Kyung Moon Sa, Seoul, 2012.
11 J.-H. Yang, A note on Maass-Jacobi forms II, Kyungpook Math. J. 53 (2013), no. 1, 49-86.   DOI
12 J.-H. Yang, Geometry and arithmetic on the Siegel-Jacobi space, Geometry and Analysis on Manifolds, In Memory of Professor Shoshichi Kobayashi (edited by T. Ochiai, A. Weinstein et al), Progress in Mathematics, Volume 308, 275-325 Birkhauser, Springer International Publishing AG Switzerland, 2015.
13 J.-H. Yang, Covariant maps for the Schrodinger-Weil representation, Bull. Korean Math. Soc. 52 (2015), no. 2, 627-647.   DOI
14 J.-H. Yang, Y.-H. Yong, S.-N. Huh, J.-H. Shin, and G.-H. Min, Sectional curvatures of the Siegel-Jacobi space, Bull. Korean Math. Soc. 50 (2013), no. 3, 787-799.   DOI
15 C. Ziegler, Jacobi forms of higher degree, Abh. Math. Semin. Univ. Hambg. 59 (1989), 191-224.   DOI
16 C. L. Siegel, Indefinite quadratische Formen und Funnktionentheorie I and II, Math. Ann. 124 (1952), 364-387
17 J.-H. Yang, Invariant metrics and Laplacians on Siegel-Jacobi space, J. Number Theory 127 (2007), no. 1, 83-102.   DOI
18 C. L. Siegel, Gesammelte Abhandlungen, Band III, Springer-Verlag (1966), 105-142 and 154-177.
19 A. Weil, Collected Papers (1964-1978), Vol. III, Springer-Verlag, 1-69, 1979.
20 A. Pitale, Jacobi Maass forms, Abh. Math. Semin. Univ. Hambg. 79 (2009), no. 1, 87-111.   DOI
21 C. L. Siegel, Indefinite quadratische Formen und Funnktionentheorie I and II, Math. Ann. 124 (1951), 17-54   DOI
22 A. Weil, Sur certains groupes d'operateurs unitares, Acta Math. 111 (1964), 143-211   DOI
23 J.-H. Yang, Harmonic analysis on the quotient spaces of Heisenberg groups, Nagoya Math. J. 123 (1991), 103-117.   DOI
24 J.-H. Yang, The Siegel-Jacobi operator, Abh. Math. Sem. Univ. Hamburg 63 (1993), 135-146.   DOI
25 J.-H. Yang, Remarks on Jacobi forms of higher degree, Proc. of the 1993 Workshop on Automorphic Forms and Related Topics, the Pyungsan Institute for Mathematical Sciences, Seoul, 33-58, 1993.
26 J.-H. Yang, Harmonic analysis on the quotient Spaces of Heisenberg groups II, J. Number Theory 49 (1994), no. 1, 63-72.   DOI
27 J.-H. Yang, Singular Jacobi forms, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2041-2049.   DOI
28 J.-H. Yang, Construction of vector valued modular forms from Jacobi forms, Canad. J. Math. 47 (1995), no. 6, 1329-1339.   DOI
29 J.-H. Yang, A decomposition theorem on differential polynomials of theta functions of high level, Japa. J. Math. 22 (1996), no. 1, 37-49.   DOI
30 J.-H. Yang, Fock representations of the Heisenberg group $H^{(g,h)}_{\mathbb{R}}$, J. Korean Math. Soc. 34 (1997), no. 2, 345-370.
31 J.-H. Yang, Lattice representations of Heisenberg groups, Math. Ann. 317 (2000), no. 2, 309-323.   DOI
32 J.-H. Yang, A note on a fundamental domain for Siegel-Jacobi space, Houston J. Math. 32 (2006), no. 3, 701-712.