Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point

Pomykała, Jacek

Non-vanishing of

n

-th derivatives of twisted elliptic

L

-functions in the critical point

Pomykała, Jacek

Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 1, pp. 1-10.

Résumé
Abstract

On note $L^{(n)} (s, E)$ la dérivée $n$ -ième de la série $L$ de Hasse-Weil associée à une courbe elliptique modulaire $E$ définie sur $ℚ$ . On évalue dans cet article le nombre de tordues $E_{d}, d \leq D$ , de la courbe elliptique $E$ telles que $L^{(n)} (1, E_{d}) \neq 0$ .

Let $E$ be a modular elliptic curve over $ℚ$ $L^{(n)} (s, E)$ denote the $n$ -th derivative of its Hasse-Weil $L$ -series. We estimate the number of twisted elliptic curves $E_{d}, d \leq D$ such that $L^{(n)} (1, E_{d}) \neq 0$ .

Zbl

@article{JTNB_1997__9_1_1_0,
     author = {Pomyka{\l}a, Jacek},
     title = {Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {1--10},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {1},
     year = {1997},
     zbl = {0889.11016},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1997__9_1_1_0/}
}

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Pomykała, Jacek. Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point. Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 1, pp. 1-10. http://archive.numdam.org/item/JTNB_1997__9_1_1_0/

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