Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Zev Klagsbrun"'
Publikováno v:
MIT web domain
Tunisian J. Math. 2, no. 2 (2020), 287-307
Tunisian J. Math. 2, no. 2 (2020), 287-307
For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgrou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a521a5393d4d4e1c199741683cc362f4
https://hdl.handle.net/1721.1/136644
https://hdl.handle.net/1721.1/136644
Autor:
Noam D. Elkies, Zev Klagsbrun
We present rank-record breaking elliptic curves having torsion subgroups Z/2Z, Z/3Z, Z/4Z, Z/6Z, and Z/7Z.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dcc4d4a6cb899ce077118590c10b0c6a
Publikováno v:
Duke Math. J. 168, no. 15 (2019), 2951-2989
For an abelian variety $A$ over a number field $F$ , we prove that the average rank of the quadratic twists of $A$ is bounded, under the assumption that the multiplication-by- $3$ -isogeny on $A$ factors as a composition of $3$ -isogenies over $F$ .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc4bc1bcd417ef29f4454150b507d50a
https://doi.org/10.1215/00127094-2019-0031
https://doi.org/10.1215/00127094-2019-0031
Let $A$ be an abelian variety over a number field $F$ and let $p$ be a prime. Cohen-Lenstra-Delaunay-style heuristics predict that the Tate-Shafarevich group of $A_s$ should contain an element of order $p$ for a positive proportion of quadratic twist
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e5aeb8c58993ace4115bfcd4b26915d
http://arxiv.org/abs/1904.00116
http://arxiv.org/abs/1904.00116
Autor:
Robert J. Lemke Oliver, Zev Klagsbrun
Publikováno v:
Mathematika. 62:67-78
This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny defined over its
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a82faa5515000a8c5d4c5a72241889d
https://doi.org/10.1112/s0025579315000121
https://doi.org/10.1112/s0025579315000121
In 2006, Elkies presented an elliptic curve with 28 independent rational points. We prove that subject to GRH, this curve has Mordell-Weil rank equal to 28 and analytic rank at most 28. We prove similar results for a previously unpublished curve of E
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a498e4e26e56014c537fe94cee0110f8
Autor:
Zev Klagsbrun
Publikováno v:
Mathematical Research Letters. 19:1137-1143
For any number field K with a complex place, we present an infinite family of elliptic curves defined over K such that dimF2 Sel2(E F /K) ≥ dimF2 E F (K)(2) + r2 for every quadratic twist E F of every curve E in this family, where r2 is the number
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::191492cfa0b77351f5289caa21e95e03
https://doi.org/10.4310/mrl.2012.v19.n5.a14
https://doi.org/10.4310/mrl.2012.v19.n5.a14
Autor:
Robert J. Lemke Oliver, Zev Klagsbrun
Publikováno v:
Research in the Mathematical Sciences. 1
In recent work, Bhargava and Shankar have shown that the average size of the 2-Selmer group of an elliptic curve overQ is exactly 3, and Bhargava and Ho have shown that the average size of the 2-Selmer group in the family of elliptic curves with a ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::72cb2c5b9ff7e5fbdf3ce1ae46312bbb
https://doi.org/10.1186/s40687-014-0015-4
https://doi.org/10.1186/s40687-014-0015-4
We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We prove that the fraction of twists (of a given elliptic curve over a fixed number field) having even 2-Selmer
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3aeae6c06c2f79b5a68e4d6ce7a395bd
http://arxiv.org/abs/1111.2321
http://arxiv.org/abs/1111.2321