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Friday, March 20, 2015 - 16:00 to 17:00
Conference Room (skype)
Dr. Karam Deo Shankhadha
Universidad de Chile, Chile
Converse theorem for Jacobi cusp forms
Abstract: In the theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to represent an automorphic form. Studying the connection between the functions that satisfy certain automorphic property and the functional equation of their associated Dirichlet series has a long history. In 1936, E. Hecke showed an outstanding equivalence between the automorphy of a cusp form $f$ and the functional equation satisfied by certain Dirichlet series $L(f,s)$ associated to $f$. Inspired by Hecke's work, a number of people got interested in studying the converse theorem for various automorphic forms. Jacobi cusp form is a classical example of an automorphic form. Y. Martin (JNT 61 (1996), 181--193) established a converse theorem for Jacobi cusp form of degree $1$ defined on $\mathcal{H} \times \mathbb{C}$ by investigating finitely many Dirichlet series associated to it. In this talk, we discuss a converse theorem for Jacobi cusp form of degree $2$ defined on $\mathcal{H}_2 \times \mathbb{C}^2$, where $\mathcal{H}_2$ denotes the Siegel upper half-space of degree $2$ and $\mathbb{C}^{2}$ is the set of all $1\times 2$ row vectors with entries in $\mathbb{C}$. This is a joint work with W. Kohnen and Y. Martin.

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