Rocky Mountain Journal of Mathematics

On Transformation Laws for Theta Functions

Olav K. Richter

Full-text: Open access

Article information

Source
Rocky Mountain J. Math. Volume 34, Number 4 (2004), 1473-1481.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.rmjm/1181069809

Digital Object Identifier
doi:10.1216/rmjm/1181069809

Mathematical Reviews number (MathSciNet)
MR2095586

Zentralblatt MATH identifier
1066.11017

Citation

Richter, Olav K. On Transformation Laws for Theta Functions. Rocky Mountain J. Math. 34 (2004), no. 4, 1473--1481. doi:10.1216/rmjm/1181069809. http://projecteuclid.org/euclid.rmjm/1181069809.


Export citation

References

  • A. Andrianov and G. Maloletkin, Behavior of theta series of degree $N$ under modular substitutions, Math. USSR-Izvestija 9 (2) (1975), 227-241.
  • --------, Behavior of theta series of genus $n$ of indefinite quadratic forms under modular substitutions, Proc. Steklov Inst. Math. 4 (1980), 1-12.
  • T. Arakawa, Siegel's formula for Jacobi forms, Internat. J. Math. 4 (5) (1993), 689-719.
  • A. Ben-Israel and T. Greville, Generalized inverses: Theory and application, Wiley Interscience, New York, 1974.
  • M. Eichler, Introduction to the theory of algebraic numbers and functions, Academic Press, New York, 1966.
  • S. Friedberg, On theta functions associated to indefinite quadratic forms, J. Number Theory 23 (1986), 255-267.
  • O. Richter, A remark on the behavior of theta series of degree $n$ under modular transformations, Internat. Math. Res. Notices 7 (2001), 371-379.
  • C. Siegel, Über die analytische Theorie der quadratischen Formen, Ann. of Math. 36 (1935), 527-606.
  • --------, Indefinite quadratische Formen und Modulfunktionen, in Studies and essays presented to R. Courant on his 60th birthday, Interscience Publisher, Inc., New York, 1948, pp. 395-406.
  • --------, Indefinite quadratische Formen und Funktionentheorie I, Math. Ann. 124 (1951), 17-54.
  • N-P. Skoruppa, Developments in the theory of Jacobi forms, Acad. Sci. USSR, Inst. Appl. Math., Khabarovsk, 1990, pp. 167-185,
  • H. Stark, On the transformation formula for the symplectic theta function and applications, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 29 (1982), 1-12.
  • R. Styer, Prime determinant matrices and the symplectic theta function, Amer. J. Math. 106 (1984), 645-664.
  • C. Ziegler, Jacobi forms of higher degree, Abh. Math. Sem. Univ. Hamburg 59 (1989), 191-224.