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Modular Forms Associated to Theta Functions

Published online by Cambridge University Press:  20 November 2018

Min Ho Lee
Min Ho Lee*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614, U.S.A., e-mail: [email protected]
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Abstract

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We use the theory of Jacobi-like forms to construct modular forms for a congruence subgroup of $\text{SL}\left( 2,\,\mathbb{R} \right)$ which can be expressed as linear combinations of products of certain theta functions.

Keywords

11F1111F2733D10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 257 - 264
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Belokolos, E., Bobenko, A., Enol’skii, V., Its, A. and Matveev, V., Algebro-geometric approach to nonlinear integrable equations. Springer-Verlag, Heidelberg, 1994.Google Scholar
[2] Borcherds, R., Automorphic forms on Os+2;2(R) and infinite products. Invent. Math. 120 (1995), 120–1995.Google Scholar
[3] Cohen, P., Manin, Y. and Zagier, D., Automorphic pseudodifferential operators. Algebraic aspects of nonlinear systems, Birkhäuser, Boston, 1997, 17–47.Google Scholar
[4] Conway, J. and Sloane, N., Sphere packings, lattices and groups. third ed., Springer-Verlag, Heidelberg, 1999.Google Scholar
[5] Dickey, L., Soliton equations and Hamiltonian systems. World Scientific, Singapore, 1991.Google Scholar
[6] Dong, C. and Mason, G., Transformation laws for theta functions. Preprint (math.QA/9903107).Google Scholar
[7] Ebeling, W., Lattices and codes. Vieweg, Braunschweig, 1994.Google Scholar
[8] Eichler, M. and Zagier, D., The theory of Jacobi forms. Progress in Math. 55, Birkhäuser, Boston, 1985.Google Scholar
[9] Mumford, D., Tata lectures on theta II. Birkhäuser, Boston, 1984.Google Scholar
[10] Schoeneberg, B., Elliptic modular functions. Springer-Verlag, Heidelberg, 1974.Google Scholar
[11] Zagier, D., Introduction to modular forms. From number theory to physics (eds., M.Waldschmidt, P. Moussa, J. Luck and C. Itzykson), Springer-Verlag, Heidelberg, 1992, 238–291.Google Scholar
[12] Zagier, D., Modular forms and differential operators. Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 104–1994.Google Scholar