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Synopsis
We review the history of elliptic curves and show that it is possible to form a group law using the points on an elliptic curve over some field L. We review various methods for computing the order of this group when L is finite, including the complex multiplication method. We then define and examine the properties of elliptic pairs, lists, and cycles, which are related to the notions of amicable pairs and aliquot cycles for elliptic curves, defined by Silverman and Stange. We then use the properties of elliptic pairs to prove that aliquot cycles of length greater than two exist for elliptic curves with complex multiplication, contrary to an assertion of Silverman and Stange, proving that such cycles only occur for elliptic curves of j-invariant equal to zero, and they always have length six. We explore the connection between elliptic pairs and several other conjectures, and propose limitations on the lengths of elliptic lists.
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Aliquot Cycles for Elliptic Curves with Complex Multiplication
Edité par
CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Neuf
Couverture souple
Vendeur : California Books, Miami, FL, Etats-Unis
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Etat : New. Print on Demand. N° de réf. du vendeur I-9781483902326
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Aliquot Cycles for Elliptic Curves with Complex Multiplication
Edité par
Createspace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Neuf
Paperback / softback
Vendeur : THE SAINT BOOKSTORE, Southport, Royaume-Uni
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Paperback / softback. Etat : New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 249. N° de réf. du vendeur C9781483902326
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
Edité par
CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Ancien ou d'occasion
Couverture souple
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
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Etat : As New. Unread book in perfect condition. N° de réf. du vendeur 37414867
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
Edité par
CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Neuf
Couverture souple
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Etat : New. N° de réf. du vendeur 37414867-n
Quantité disponible : Plus de 20 disponibles
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
Edité par
CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Neuf
Couverture souple
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
Etat : New. N° de réf. du vendeur 37414867-n
Quantité disponible : Plus de 20 disponibles
Image fournie par le vendeur
Aliquot Cycles for Elliptic Curves With Complex Multiplication
Edité par
CreateSpace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Ancien ou d'occasion
Couverture souple
Vendeur : GreatBookPricesUK, Woodford Green, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
Etat : As New. Unread book in perfect condition. N° de réf. du vendeur 37414867
Quantité disponible : Plus de 20 disponibles
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Aliquot Cycles for Elliptic Curves with Complex Multiplication (Paperback)
Edité par
Createspace Independent Publishing Platform, 2013
ISBN 10 : 1483902323
ISBN 13 : 9781483902326
Neuf
Paperback
Vendeur : CitiRetail, Stevenage, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
Paperback. Etat : new. Paperback. We review the history of elliptic curves and show that it is possible to form a group law using the points on an elliptic curve over some field L. We review various methods for computing the order of this group when L is finite, including the complex multiplication method. We then define and examine the properties of elliptic pairs, lists, and cycles, which are related to the notions of amicable pairs and aliquot cycles for elliptic curves, defined by Silverman and Stange. We then use the properties of elliptic pairs to prove that aliquot cycles of length greater than two exist for elliptic curves with complex multiplication, contrary to an assertion of Silverman and Stange, proving that such cycles only occur for elliptic curves of j-invariant equal to zero, and they always have length six. We explore the connection between elliptic pairs and several other conjectures, and propose limitations on the lengths of elliptic lists. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9781483902326
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