Given any integer
Étant donné un entier
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Accepté le :
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Mots-clés : Elliptic curves, Complex multiplication, Tate–Shafarevich group,
Yukako Kezuka 1

@article{JTNB_2021__33_3.2_945_0, author = {Yukako Kezuka}, title = {Tamagawa number divisibility of central $L$-values of twists of the {Fermat} elliptic curve}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {945--970}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {33}, number = {3.2}, year = {2021}, doi = {10.5802/jtnb.1183}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1183/} }
TY - JOUR AU - Yukako Kezuka TI - Tamagawa number divisibility of central $L$-values of twists of the Fermat elliptic curve JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 945 EP - 970 VL - 33 IS - 3.2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1183/ DO - 10.5802/jtnb.1183 LA - en ID - JTNB_2021__33_3.2_945_0 ER -
%0 Journal Article %A Yukako Kezuka %T Tamagawa number divisibility of central $L$-values of twists of the Fermat elliptic curve %J Journal de théorie des nombres de Bordeaux %D 2021 %P 945-970 %V 33 %N 3.2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1183/ %R 10.5802/jtnb.1183 %G en %F JTNB_2021__33_3.2_945_0
Yukako Kezuka. Tamagawa number divisibility of central $L$-values of twists of the Fermat elliptic curve. Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 3.2, pp. 945-970. doi : 10.5802/jtnb.1183. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1183/
[1] Notes on elliptic curves. II, J. Reine Angew. Math., Volume 218 (1965), pp. 79-108 | MR | Zbl
[2] The Magma algebra system. I. The user language, J. Symb. Comput., Volume 24 (1997) no. 3-4, pp. 235-265 | DOI | MR | Zbl
[3] Cube sum problem and an explicit Gross-Zagier formula, Am. J. Math., Volume 139 (2017) no. 3, pp. 785-816 | DOI | MR | Zbl
[4] Arithmetic on curves of genus 1. IV. Proof of the Hauptvermutung, J. Reine Angew. Math., Volume 211 (1962), pp. 95-112 | MR | Zbl
[5] Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer, J. Reine Angew. Math., Volume 217 (1965), pp. 180-199 | MR | Zbl
[6] Lectures on the Birch–Swinnerton-Dyer conjecture, ICCM Not., Volume 1 (2013) no. 2, pp. 29-46 | DOI | MR
[7] Séries d’Eisenstein et fonctions
[8] On the
[9] A classical family of elliptic curves having rank one and the
[10] Reciprocity Laws. From Euler to Eisenstein, Springer Monographs in Mathematics, Springer, 2000 | DOI
[11]
[12] Elliptic curves with CM by
[13] Variation of the root number in families of elliptic curves, Compos. Math., Volume 87 (1993) no. 2, pp. 119-151 | Numdam | MR | Zbl
[14] Central values of L-functions of cubic twists, Math. Ann., Volume 378 (2020) no. 3-4, pp. 1327-1370 | DOI | MR | Zbl
[15] The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Invent. Math., Volume 103 (1991) no. 1, pp. 25-68 | DOI | MR | Zbl
[16] Groupes de Selmer et corps cubiques, J. Number Theory, Volume 23 (1986) no. 3, pp. 294-317 | DOI | MR | Zbl
[17] Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, 151, Springer, 1994 | DOI
[18] The diophantine equation
[19] Algorithm for determining the type of a singular fiber in an elliptic pencil, Modular functions of one variable. IV (Lecture Notes in Mathematics), Volume 476, Springer, 1975, pp. 33-52 | DOI | MR | Zbl
[20] SageMath, the Sage Mathematics Software System (Version 9.0), 2020 (http://www.sagemath.org/)
[21] Density of rational points on isotrivial rational elliptic surfaces, Algebra Number Theory, Volume 5 (2011) no. 5, pp. 659-690 | DOI | MR | Zbl
[22] Numerical investigations related to the
[23] The nonvanishing of
[24] A criterion for elliptic curves with second lowest 2-power in
- Lower bound for the 2-adic valuations of central
-values of elliptic curves with complex multiplication, Kyushu Journal of Mathematics, Volume 78 (2024) no. 1, pp. 47-69 | DOI:10.2206/kyushujm.78.47 | Zbl:7898736 - On central
-values and the growth of the -part of the Tate-Shafarevich group, International Journal of Number Theory, Volume 19 (2023) no. 4, pp. 785-802 | DOI:10.1142/s1793042123500392 | Zbl:1530.11055
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