Algebraic divisibility sequences over function fields
Ingram, Patrick, Mage, Valery, Silverman, Joseph H., Stange, Katherine E. and Streng, Marco. (2012) Algebraic divisibility sequences over function fields. Journal of the Australian Mathematical Society, Vol.92 . pp. 1-28. ISSN 1446-7887Full text not available from this repository.
Official URL: http://dx.doi.org/10.1017/S1446788712000092
In this note we study the existence of primes and of primitive divisors in function ﬁeld analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function ﬁelds deﬁned over number ﬁelds contain inﬁnitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function ﬁeld has only ﬁnitely many terms lacking a primitive divisor.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Journal of the Australian Mathematical Society|
|Publisher:||Cambridge University Press|
|Page Range:||pp. 1-28|
|Access rights to Published version:||Restricted or Subscription Access|
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