Name: Aliquot Cycles for Elliptic Curves with Complex Multiplication (en Inglés)
Price: 53457.00 COP
Availability: InStock
Author: Morrell, Thomas
ISBN: 9781483902326

portada Aliquot Cycles for Elliptic Curves with Complex Multiplication (en Inglés)

Formato

Libro Físico

Autor

Thomas Morrell

Editorial

Createspace Independent Publishing Platform

Idioma

Inglés

N° páginas

Encuadernación

Tapa Blanda

Dimensiones

27.9 x 21.6 x 0.3 cm

Peso

0.16 kg.

ISBN13

9781483902326

Categorías

Teoría de números

Aliquot Cycles for Elliptic Curves with Complex Multiplication (en Inglés)

Thomas Morrell (Autor) · Createspace Independent Publishing Platform · Tapa Blanda

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Origen: Estados Unidos (Costos de importación incluídos en el precio)

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Reseña del libro "Aliquot Cycles for Elliptic Curves with Complex Multiplication (en Inglés)"

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.