The uniform primality conjecture for elliptic curves
Acta Arithmetica(2008)
摘要
An elliptic divisibility sequence, generated by a point in the image of a
rational isogeny, is shown to possess a uniformly bounded number of prime
terms. This result applies over the rational numbers, assuming Lang's
conjecture, and over the rational function field, unconditionally. In the
latter case, a uniform bound is obtained on the index of a prime term.
Sharpened versions of these techniques are shown to lead to explicit results
where all the irreducible terms can be computed.
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关键词
prime,. canonical height,divisibility sequence,elliptic curve,division polynomial,isogeny,rational function field,siegel's theorem.,reduction,rational number,rational function,elliptic divisibility sequence
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