SIEGEL MODULAR FORMS OF GENUS 2 ATTACHED TO ELLIPTIC CURVES

By Dinakar Ramakrishnan, F. Shahidi. 2006

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The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in which case the degree 4 spinor L-function L(s, F ) is divisible by an abelian L-function, nor of Yoshida type, in which case L(s, F ) is a product of L-series of a pair of elliptic cusp forms. In other words, for each F in the class of holomorphic Siegel cusp forms we construct below, which includes those of scalar weight ≥ 3, the cuspidal automorphic representation π of GSp(4,A) generated by F is neither CAP, short for Cuspidal Associated to a Parabolic, nor endoscopic, i.e., one arising as the transfer of a cusp form on GL(2)×GL(2), and consequently, L(s, F ) is not a product of L-series of smaller degrees. A key example of the first kind of Siegel modular forms we construct is furnished by the following result, which will be used in [34]:

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2fc9a50a4e1c722c147e47467fbd89fe2d6ad3a8

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Citations in the corpus

Siegel modular forms of degree three and the cohomology of local systems (2011, background): “It is shown in [45] that there is a Siegel modular form f of degree 2 and weight (10, 13) such that λp( f ) = Tr ( Fp, Sym3(S[12]) ) for all primes p.”