On symplectic Euler factors of genus two

“…Throughout this article, when we write M k (K(N ) * , χ), the weight k is in Z ≥0 , the level N is in N and the character χ is an Atkin-Lehner character. We define, following [17], the standard groups Γ 0 (N ) = K(N ) ∩ Sp 2 (Z) and…”

Section: Siegel Modular Forms and Notationmentioning

confidence: 99%

Computations of Spaces of Paramodular Forms of General Level

Breeding¹,

Poor²,

Yuen³

2016

Journal of the Korean Mathematical Society

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Abstract. This article gives upper bounds on the number of FourierJacobi coefficients that determine a paramodular cusp form in degree two. The level N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.

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“…Specifically, using [13], one can define the action of the operator T (q δ ) for S k (Γ para [p]) for primes (p, q) = 1. Suppose we are given a paramodular form F ∈ S k (Γ para [p]) so that for all n ∈ Z, F | T (n) = λ F,n F = λ n F .…”

Section: L-function Notationmentioning

confidence: 99%

A Böcherer-Type Conjecture for Paramodular Forms

Ryan

Tornaría

2011

Int. J. Number Theory

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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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On symplectic Euler factors of genus two

Cited by 19 publications

References 10 publications

On Siegel modular forms part II

On Siegel modular forms part II

Computations of Spaces of Paramodular Forms of General Level

A Böcherer-Type Conjecture for Paramodular Forms

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