An explicit Waldspurger formula for Hilbert modular forms

Sirolli, Nicolás; Tornaría, Gonzalo

doi:10.1090/tran/7112

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Theorem A follows from Theorem B by choosing l such that L(1/2, g ⊗ χ l ) = 0 and letting f γ = ϑ l,χ (ϕ g ) (see Section 6 for the details). The proof of Theorem B relies on our previous articles [ST18,ST20], which made strong restrictions on the functions γ, as well as on the weight and on the signs ε g (v), that we now lift. It is based on the results from [Zha01,Xue06] giving central values in terms of height parings, which we relate to Fourier coefficients.…”

Section: Introductionmentioning

confidence: 99%

Effective construction of Hilbert modular forms of half-integral weight

Sirolli¹,

Tornaría²

2021

Preprint

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Given a Hilbert cuspidal newform g we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted L-series of g by fundamental discriminants.The family is parametrized by quadratic conditions on the primes dividing the level of g, where each form has coefficients supported on the discriminants satisfying the conditions. These modular forms are given as generalized theta series and thus their coefficients can be effectively computed.Our construction works over arbitrary totally real number fields, except that in the case of odd degree the square levels are excluded. It includes all discriminants except those divisible by primes whose square divides the level.

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