ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS

作者：Ingram Patrick; Mahe Valery; Silverman Joseph H^*; Stange Katherine E; Streng Marco

来源：Journal of the Australian Mathematical Society, 2012, 92(1): 99-126.

DOI：10.1017/S1446788712000092

• lucas sequence
• elliptic divisibility sequence
• primitive divisor
• function field over number field

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.

• 出版日期2012-2