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arXiv · 2205.06685

Higher Reciprocity Laws and Ternary Linear Recurrence Sequences

Pieter Moree·Armand Noubissie
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Abstract

We describe the set of prime numbers splitting completely in the non-abelian splitting field of certain monic irreducible polynomials of degree three. As an application we establish some divisibility properties of the associated ternary recurrence sequence by primes $p$, thus greatly extending recent work of Evink and Helminck and of Faisant. We also prove some new results on the number of solutions of the characteristic equation of the recurrence sequence modulo $p,$ extending and simplifying earlier work of Zhi-Hong Sun (2003).

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Pieter Moree, Armand Noubissie. 2022-05-13. Higher Reciprocity Laws and Ternary Linear Recurrence Sequences. https://arxiv.org/abs/2205.06685

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