Výsledky vyhledávání - "Joseph L. Wetherell"

Linear independence in linear systems on elliptic curves

Autor: Bradley W. Brock, A. J. Scholl, Bjorn Poonen, Joseph L. Wetherell, Bruce W. Jordan

Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic subgroup of odd order $N$, over an algebraically closed field $k$ with $\operatorname{char} k \nmid N$. For $P \in C$, let $s_P$ be a rational function with divisor $N \cdot P -

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1a00a73e8ba5ea3562ba10602c4c7d3
https://www.repository.cam.ac.uk/handle/1810/325259

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Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

Autor: E. Victor Flynn, Joseph L. Wetherell, Edward F. Schaefer, Franck Leprévost, William Stein, Michael Stoll

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::20bb677957798b314ee1369a034099f2
https://ora.ox.ac.uk/objects/uuid:e23f4731-cd7f-4e6b-807d-65e7fc6a982b

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On torsion in abelian varieties

Autor: Sheldon Kamienny, Joseph L. Wetherell

Publikováno v: Communications in Algebra. 26:1675-1678

(1998). On torsion in abelian varieties. Communications in Algebra: Vol. 26, No. 5, pp. 1675-1678.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b132c7adbae0f7f8b5266615da787bba
https://doi.org/10.1080/00927879808826230

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Polynomials with a common composite

Autor: Robert Beals, Joseph L. Wetherell, Michael E. Zieve

Let f and g be nonconstant polynomials over an arbitrary field K. In this paper we study the intersection of the polynomial rings K[f] and K[g], and in particular we ask whether this intersection is larger than K. We completely resolve this question

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::33d22f23ce9f52fd370498141b69cb31
http://arxiv.org/abs/0707.1552

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Curves of every genus with many points. II. Asymptotically good families

Autor: Everett W. Howe, Noam D. Elkies, Michael E. Zieve, Joseph L. Wetherell, Bjorn Poonen, Andrew Kresch

Publikováno v: Duke Math. J. 122, no. 2 (2004), 399-422

We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a positive constant c_q with the following property: for every non-negat

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::880169121300a4d177e2438eba61bc0b
https://www.zora.uzh.ch/id/eprint/21789/

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Finding rational points on bielliptic genus 2 curves

Autor: E. V. Flynn, Joseph L. Wetherell

Publikováno v: Scopus-Elsevier

We discuss a technique for trying to find all rational points on curves of the form Y 2=f 3 X 6+f 2 X 4+f 1 X 2+f 0, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or 1, Chabauty's

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::76f733ef5d9dc9f4ce65d457157702d9
http://ora.ox.ac.uk/objects/uuid:b4693b65-ac41-4b8d-b5f1-24fa4bf597ec

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Computing the Selmer group of an isogeny between Abelian varieties using a further isogeny to a Jacobian

Autor: Joseph L. Wetherell, Edward F. Schaefer

Publikováno v: Journal of Number Theory. (1):158-175

This article describes an algorithm for computing the Selmer group of an isogeny between abelian varieties. This algorithm applies when there is an isogeny from the image abelian variety to the Jacobian of a curve. The use of an auxiliary Jacobian si

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Covering collections and a challenge problem of Serre

Autor: E. Victor Flynn, Joseph L. Wetherell

Publikováno v: Scopus-Elsevier

We answer a challenge of Serre by showing that every rational point on the projective curve X$^4$ + Y$^4$ = 17 Z$^4$ is of the form ($\pm$1, $\pm$2, 1) or ($\pm$2, $\pm$1, 1). Our approach builds on recent ideas from both Nils Bruin and the authors o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea8c1a07eb449483d44b95df35a3e0fe
http://www.scopus.com/inward/record.url?eid=2-s2.0-0035651862&partnerID=MN8TOARS

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Akademický článek

A p-adic approach to rational points on curves.

Autor: Poonen, Bjorn¹ (AUTHOR)

Publikováno v: Bulletin (New Series) of the American Mathematical Society. jan2021, Vol. 58 Issue 1, p45-56. 12p.

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