On Formal Series of Jacobi Forms and Borcherds Products
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By Fourier-Jacobi expansion, a Siegel modular form of degree 2 gives a family of Jacobi forms of weight k and index \(0,1,2,3,\ldots\). By the translation formula of Siegel modular forms, these Jacobi forms have a kind of symmetry. In this paper, we give one conjecture on the Fourier-Jacobi expansion that is true for Siegel modular forms with small levels. Our conjecture is useful to show the convergence of Maass lifts and Borcherds products.
Mathematics Subject Classification 2000Primary 11F50 Secondary 11F46
This paper is based on the talk at International Workshop on Mathematics 2012 at Muscat in Oman, organized by Sultan Qaboos University and the German University of Technology. The author would like to thank the organizers Professor Bernherd Heim, Professor Mehiddin Al-Baali and Professor Tomoyoshi Ibukiyama for giving me a chance to talk about my researches in such a nice conference. Also the author would like to thank the referee for carefully reading our manuscript and for giving some constructive comments.
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