414 research outputs found
A B\"ocherer-Type Conjecture for Paramodular Forms
In the 1980s B\"ocherer 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
GL2xGSp2 L-values and Hecke eigenvalue congruences
We find experimental examples of congruences of
Hecke eigenvalues between automorphic representations of groups such as GSp2(A), SO(4, 3)(A) and SO(5, 4)(A), where the prime modulus should, for various reasons, appear in the algebraic part of a critical “tensor-product” L-value associated to cuspidal automorphic representations of GL2(A) and GSp2
(A). Using special techniques for evaluating L-functions with few known coefficients, we compute sufficiently good approximations to detect the anticipated prime divisors
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