Matches in SemOpenAlex for { <https://semopenalex.org/work/W2896576844> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W2896576844 abstract "Given an elliptic curve $E/mathbb{Q}$, it is a conjecture of Goldfeld that asymptotically half of its quadratic twists will have rank zero and half will have rank one. Nevertheless, higher rank twists do occur: subject to the parity conjecture, Gouv^ea and Mazur constructed $X^{1/2-epsilon}$ twists by discriminants up to $X$ with rank at least two. For any $dgeq 3$, we build on their work to consider twists by degree $d$ $S_d$-extensions of $mathbb{Q}$ with discriminant up to $X$. We prove that there are at least $X^{c_d-epsilon}$ such twists with positive rank, where $c_d$ is a positive constant that tends to $1/4$ as $dtoinfty$. Moreover, subject to a suitable parity conjecture, we obtain the same result for twists with rank at least two." @default.
- W2896576844 created "2018-10-26" @default.
- W2896576844 creator A5022859546 @default.
- W2896576844 creator A5043912491 @default.
- W2896576844 date "2018-10-09" @default.
- W2896576844 modified "2023-09-27" @default.
- W2896576844 title "Rank growth of elliptic curves in nonabelian extensions" @default.
- W2896576844 cites W1535303174 @default.
- W2896576844 cites W162753765 @default.
- W2896576844 cites W2014191379 @default.
- W2896576844 cites W2030859474 @default.
- W2896576844 cites W2050964750 @default.
- W2896576844 hasPublicationYear "2018" @default.
- W2896576844 type Work @default.
- W2896576844 sameAs 2896576844 @default.
- W2896576844 citedByCount "0" @default.
- W2896576844 crossrefType "posted-content" @default.
- W2896576844 hasAuthorship W2896576844A5022859546 @default.
- W2896576844 hasAuthorship W2896576844A5043912491 @default.
- W2896576844 hasConcept C109214941 @default.
- W2896576844 hasConcept C114614502 @default.
- W2896576844 hasConcept C121332964 @default.
- W2896576844 hasConcept C129844170 @default.
- W2896576844 hasConcept C154945302 @default.
- W2896576844 hasConcept C164226766 @default.
- W2896576844 hasConcept C179603306 @default.
- W2896576844 hasConcept C202444582 @default.
- W2896576844 hasConcept C2524010 @default.
- W2896576844 hasConcept C2777151079 @default.
- W2896576844 hasConcept C2780990831 @default.
- W2896576844 hasConcept C33923547 @default.
- W2896576844 hasConcept C41008148 @default.
- W2896576844 hasConcept C78397625 @default.
- W2896576844 hasConceptScore W2896576844C109214941 @default.
- W2896576844 hasConceptScore W2896576844C114614502 @default.
- W2896576844 hasConceptScore W2896576844C121332964 @default.
- W2896576844 hasConceptScore W2896576844C129844170 @default.
- W2896576844 hasConceptScore W2896576844C154945302 @default.
- W2896576844 hasConceptScore W2896576844C164226766 @default.
- W2896576844 hasConceptScore W2896576844C179603306 @default.
- W2896576844 hasConceptScore W2896576844C202444582 @default.
- W2896576844 hasConceptScore W2896576844C2524010 @default.
- W2896576844 hasConceptScore W2896576844C2777151079 @default.
- W2896576844 hasConceptScore W2896576844C2780990831 @default.
- W2896576844 hasConceptScore W2896576844C33923547 @default.
- W2896576844 hasConceptScore W2896576844C41008148 @default.
- W2896576844 hasConceptScore W2896576844C78397625 @default.
- W2896576844 hasLocation W28965768441 @default.
- W2896576844 hasOpenAccess W2896576844 @default.
- W2896576844 hasPrimaryLocation W28965768441 @default.
- W2896576844 hasRelatedWork W1621867678 @default.
- W2896576844 hasRelatedWork W1794186343 @default.
- W2896576844 hasRelatedWork W1993121135 @default.
- W2896576844 hasRelatedWork W2094784757 @default.
- W2896576844 hasRelatedWork W2106529737 @default.
- W2896576844 hasRelatedWork W2143145642 @default.
- W2896576844 hasRelatedWork W2260533153 @default.
- W2896576844 hasRelatedWork W2269377580 @default.
- W2896576844 hasRelatedWork W2528498428 @default.
- W2896576844 hasRelatedWork W2950579761 @default.
- W2896576844 hasRelatedWork W2953179406 @default.
- W2896576844 hasRelatedWork W2963270550 @default.
- W2896576844 hasRelatedWork W2979826598 @default.
- W2896576844 hasRelatedWork W2980799738 @default.
- W2896576844 hasRelatedWork W2981859449 @default.
- W2896576844 hasRelatedWork W2989567396 @default.
- W2896576844 hasRelatedWork W2995795483 @default.
- W2896576844 hasRelatedWork W3037742570 @default.
- W2896576844 hasRelatedWork W3128779604 @default.
- W2896576844 hasRelatedWork W3213151471 @default.
- W2896576844 isParatext "false" @default.
- W2896576844 isRetracted "false" @default.
- W2896576844 magId "2896576844" @default.
- W2896576844 workType "article" @default.