Algebraic divisibility sequences over function fields
Number Theory
2014-12-30 v2 Algebraic Geometry
Abstract
We study the existence of primes and of primitive divisors in classical divisibility sequences defined over function fields. 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.
Keywords
Cite
@article{arxiv.1105.5633,
title = {Algebraic divisibility sequences over function fields},
author = {Patrick Ingram and Valéry Mahé and Joseph H. Silverman and Katherine E. Stange and Marco Streng},
journal= {arXiv preprint arXiv:1105.5633},
year = {2014}
}
Comments
28 pages