Eisenstein Series for Jacobi Forms of Lattice Index
Heilbronn Number Theory Seminar
11th October 2017, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
Jacobi forms arise naturally in number theory in several ways: theta functions arise as functions of lattices and Siegel modular forms give rise to Jacobi forms through their Fourier-Jacobi expansion, for example. Jacobi forms of lattice index appear in the theory of reflective modular forms and that of vertex operator algebras. In this talk, we introduce Eisenstein series for Jacobi forms of lattice index and we state some of their properties. We compute their Fourier expansions and we give an explicit formula for the Fourier coefficients of the trivial Eisenstein series. We show that, for even weight and fixed index, finite linear combinations of Fourier coefficients of non-trivial Eisenstein series are equal to finite linear combinations of Fourier coefficients of the trivial one.