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DC Field | Value | Language |
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dc.contributor.author | Tomasz Jedrzejak | - |
dc.date.accessioned | 2024-02-27T05:57:04Z | - |
dc.date.available | 2024-02-27T05:57:04Z | - |
dc.date.issued | 2019 | - |
dc.identifier.uri | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/6369 | - |
dc.description.abstract | The title equations are connected with Jacobians of hyperelliptic curves Cm,a,b : y2 = x 2m + ax + b defined over (Ql. More precisely, these equations have a nontrivial solution if and only if the class of the divisor oo+ - oo- is a torsion point in Jacobian Jac(Cm,a,b), where oo+ and oo- are two points at infinity in Cm,a,b• We show that if ab = 0 then the title equations have nontrivial solutions (and we write explicit formulae). On the other hand, we prove that for any m. > 1 there exist infinitely many pairs (a, b) such that our equations have no nontrivial solutions. Moreover, form = 2, 3 for almost all (a, b) with ab i= 0, these equations have no nontrivial solutions. We also give infinitely many explicit examples when nontrivial solution does not exist. | - |
dc.publisher | Journal of the Ramanujan Mathematical Society | - |
dc.title | Polynomial Pell equations P x2 – x2m + b Q x2 and associated hyperelliptic curves | - |
dc.vol | Vol 34 | - |
dc.issued | No 2 | - |
Appears in Collections: | Articles to be qced |
Files in This Item:
File | Size | Format | |
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Polynomial Pell equations P x 2.pdf Restricted Access | 407.32 kB | Adobe PDF | View/Open Request a copy |
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