Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Harris B. Daniels"'
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 22-52 (2019)
Abstract Recently, there has been much interest in studying the torsion subgroups of elliptic curves base‐extended to infinite extensions of Q. In this paper, given a finite group G, we study what happens with the torsion of an elliptic curve E ove
Externí odkaz:
https://doaj.org/article/a750fea942244e84828ebf3f0efab1b2
Autor:
Harris B. Daniels
Publikováno v:
Journal of Algebra. 575:274-284
In [2] , the author claims that the fields Q ( D 4 ∞ ) defined in the paper and the compositum of all D 4 extensions of Q coincide. The proof of this claim depends on a misreading of a celebrated result by Shafarevich. The purpose is to salvage the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7020e672b25b82fb19f25ae943047d50
https://doi.org/10.1016/j.jalgebra.2021.02.008
https://doi.org/10.1016/j.jalgebra.2021.02.008
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 32:231-258
In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of examples of hyperelliptic curves $C: y^2=f(x)$ defined over $\mathbb{Q}$, wi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::595c89c82f3ccf36e70dc458f79a0222
https://doi.org/10.5802/jtnb.1120
https://doi.org/10.5802/jtnb.1120
Publikováno v:
Experimental Mathematics. 31:518-536
Let $E$ be an elliptic curve without complex multiplication defined over the rationals. The purpose of this article is to define a positive integer $A(E)$, that we call the {\it Serre's constant associated to $E$}, that gives necessary conditions to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::227061ce9c763166faa92792e28d4fbe
https://doi.org/10.1080/10586458.2019.1655816
https://doi.org/10.1080/10586458.2019.1655816
Autor:
Harris B. Daniels
Publikováno v:
Journal of Algebra. 509:535-565
Let E / Q be an elliptic curve and let Q ( D 4 ∞ ) be the compositum of all extensions of Q whose Galois closure has Galois group isomorphic to a quotient of a subdirect product of a finite number of transitive subgroups of D 4 . In this article we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8448619e2a478b5497dc65fe1a39549e
https://doi.org/10.1016/j.jalgebra.2018.02.038
https://doi.org/10.1016/j.jalgebra.2018.02.038
Publikováno v:
Journal of Number Theory. 157:367-396
The theory of complex multiplication has proven to be an essential tool in number theory, mainly due to the connections with class field theory developed by Kronecker, Weber, Fricke, Hasse, Deuring, and Shimura, among others. Certain important result
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1ffecd03739aca4b592bde4ee1ca14c8
https://doi.org/10.1016/j.jnt.2015.05.009
https://doi.org/10.1016/j.jnt.2015.05.009
Publikováno v:
Notices of the American Mathematical Society. 64:241-243
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b59fbfd208255ced7776e35e9d56329
https://doi.org/10.1090/noti1490
https://doi.org/10.1090/noti1490
Given an elliptic curve $E/\mathbb{Q}$ with torsion subgroup $G = E(\mathbb{Q})_{\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\mathbb{Q}$. We also determin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b885c5720a7a159a9bc76a6e7d13ca7b
http://arxiv.org/abs/1808.02887
http://arxiv.org/abs/1808.02887
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 22-52 (2019)
Recently there has been much interest in studying the torsion subgroups of elliptic curves base-extended to infinite extensions of $\mathbb{Q}$. In this paper, given a finite group $G$, we study what happens with the torsion of an elliptic curve $E$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8849ed2aa1b248ab237bdb79f99cfab7
http://arxiv.org/abs/1803.09614
http://arxiv.org/abs/1803.09614
Autor:
Harris B. Daniels
Publikováno v:
Journal of Number Theory. 155:226-247
Given an elliptic curve E / Q , the torsion points of E give rise to a natural Galois representation ρ E : Gal ( Q ¯ / Q ) → GL 2 ( Z ˆ ) associated to E. In 1972, Serre showed that [ GL 2 ( Z ˆ ) : Im ρ E ] ≥ 2 for all non-CM elliptic curve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5a65061eb248d795bdcb7a932433ea7a
https://doi.org/10.1016/j.jnt.2015.03.016
https://doi.org/10.1016/j.jnt.2015.03.016