Dérivée en <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> de la fonction L p-adique du carré symétrique dʼune courbe elliptique sur un corps totalement réel

Rosso, Giovanni

doi:10.1016/j.crma.2013.04.007

Cited by 2 publications

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References 9 publications

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“…In this case, the form f is Steinberg at p and the trivial zero is brought by E 1 . The proof of this theorem is the natural generalization of the (unpublished) proof of Greenberg and Tilouine in the ordinary case (which has already been generalized to the Hilbert setting in [50,48]). We remark that in the forthcoming paper [49] we remove the hypothesis that N is even and allow p = 2 when k 0 = 2 using a different method.…”

Section: Introductionmentioning

confidence: 87%

A formula for the derivative of the p-adic L-function of the symmetric square of a finite slope modular form

Rosso¹

2016

American Journal of Mathematics

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Let f be a modular form of weight k and Nebentypus ψ. By generalizing a construction of [20], we construct a p-adic L-function interpolating the special values of the L-function L(s, Sym 2 (f ) ⊗ ξ), where ξ is a Dirichlet character. When s = k − 1 and ξ = ψ −1 , this p-adic L-function vanishes due to the presence of a so-called trivial zero. We give a formula for the derivative at s = k −

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Section: Introductionmentioning

confidence: 87%

A formula for the derivative of the p-adic L-function of the symmetric square of a finite slope modular form

Rosso¹

2016

American Journal of Mathematics

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“…In the case where f corresponds to an elliptic curve, such a theorem has been claimed in [Ros13a]. We were able to substitute the hypothesis p inert by there is only one prime ideal of F above p thanks to a clever remark of Éric Urban to whom we are very grateful.…”

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confidence: 88%

Derivative at s = 1 of the p-adic L-function of the symmetric square of a Hilbert modular form

Rosso

2016

Isr. J. Math.

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Let p ≥ 3 be a prime and F a totally real number field. Let f be a Hilbert cuspidal eigenform of parallel weight 2, trivial Nebentypus and ordinary at p. It is possible to construct a p-adic L function which interpolates the complex L-function associated with the symmetric square representation of f . This p-adic L-function vanishes at s = 1 even if the complex L-function does not. Assuming p inert and f Steinberg at p, we give a formula for the p-adic derivative at s = 1 of this p-adic L-function, generalizing unpublished work of Greenberg and Tilouine. Under some hypotheses on the conductor of f we prove a particular case of a conjecture of Greenberg on trivial zeros.

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Dérivée en s=1 de la fonction L p-adique du carré symétrique dʼune courbe elliptique sur un corps totalement réel

Cited by 2 publications

References 9 publications

A formula for the derivative of the p-adic L-function of the symmetric square of a finite slope modular form

A formula for the derivative of the p-adic L-function of the symmetric square of a finite slope modular form

Derivative at s = 1 of the p-adic L-function of the symmetric square of a Hilbert modular form

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