Geodesic
Integrality of twisted $L$-values of elliptic curves
Documenta mathematica, Tome 27 (2022), pp. 2041-2066.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Under suitable, fairly weak hypotheses on an elliptic curve $E/\mathbb{Q}$ and a primitive non-trivial Dirichlet character $\chi $, we show that the algebraic $L$-value $\mathscr{L}(E,\chi)$ at $s=1$ is an algebraic integer. For instance, for semistable curves $\mathscr{L}(E,\chi)$ is integral whenever $E$ admits no isogenies defined over $\mathbb{Q}$. Moreover we give examples illustrating that our hypotheses are necessary for integrality to hold.
Classification : 11G40, 11G05, 11F67
Keywords: elliptic curves, \(L\)-functions, modular symbols 
@article{DOCMA_2022__27__a14,
     author = {Wiersema, Hanneke and Wuthrich, Christian},
     title = {Integrality of twisted {\(L\)-values} of elliptic curves},
     journal = {Documenta mathematica},
     pages = {2041--2066},
     publisher = {mathdoc},
     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a14/}
}
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Wiersema, Hanneke; Wuthrich, Christian. Integrality of twisted \(L\)-values of elliptic curves. Documenta mathematica, Tome 27 (2022), pp. 2041-2066. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a14/