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Divisibility sequences for elliptic curves with complex multiplication
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Streng, Marco (2008) Divisibility sequences for elliptic curves with complex multiplication. Algebra & Number Theory, Vol.2 (No.2). pp. 183-208. doi:10.2140/ant.2008.2.183 ISSN 1937-0652.
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Official URL: http://dx.doi.org/10.2140/ant.2008.2.183
Abstract
Elliptic divisibility sequences arise as sequences of denominators of the integer multiples of a rational point on an elliptic curve. Silverman proved that almost every term of such a sequence has a primitive divisor (that is, a prime divisor that has not appeared as a divisor of earlier terms in the sequence). If the elliptic curve has complex multiplication, then we show how the endomorphism ring can be used to index a similar sequence and we prove that this sequence also has primitive divisors. The original proof fails in this context and will be replaced by an inclusion-exclusion argument and sharper diophantine estimates.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Algebra & Number Theory | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 1937-0652 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.2 | ||||
Number: | No.2 | ||||
Page Range: | pp. 183-208 | ||||
DOI: | 10.2140/ant.2008.2.183 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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