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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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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
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Aliquot Cycles for Elliptic Curves with Complex Multiplication
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ISBN 10: 1483902323
ISBN 13: 9781483902326
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
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ISBN 10: 1483902323
ISBN 13: 9781483902326
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
Verlag:
CreateSpace Independent Publishing Platform, 2013
ISBN 10: 1483902323
ISBN 13: 9781483902326
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
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CreateSpace Independent Publishing Platform, 2013
ISBN 10: 1483902323
ISBN 13: 9781483902326
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Aliquot Cycles for Elliptic Curves With Complex Multiplication
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CreateSpace Independent Publishing Platform, 2013
ISBN 10: 1483902323
ISBN 13: 9781483902326
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Aliquot Cycles for Elliptic Curves with Complex Multiplication
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Paperback. Zustand: 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. Bestandsnummer des Verkäufers 9781483902326
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