Abstract
In the 1980s Böcherer formulated a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a Siegel modular form F to the coefficients of F. He proved the conjecture when F is a Saito–Kurokawa lift. Later Kohnen and Kuß gave numerical evidence for the conjecture in the case when F is a rational eigenform that is not a Saito–Kurokawa lift. In this paper we develop a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a paramodular form and the coefficients of the form. We prove the conjecture in the case when the form is a Gritsenko lift and provide numerical evidence when it is not a lift.
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