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arXiv · 1011.1307

Testing the functional equations of a high-degree Euler product

David W. Farmer·Nathan C. Ryan·Ralf Schmidt
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Abstract

We study the L-functions associated to Siegel modular forms (equivalently, automorphic representations of ${\rm GSp}(4,\mathbb{A}_{\mathbb{Q}})$) both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform representation theoretic calculations to cast the Langlands L-function in classical terms. We develop a precise notion of what it means to test a conjectured functional equation for an L-function, and we apply this to the degree 10 adjoint L-function associated to a Siegel modular form.

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David W. Farmer, Nathan C. Ryan, Ralf Schmidt. 2010-11-05. Testing the functional equations of a high-degree Euler product. https://arxiv.org/abs/1011.1307

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