A note on the arithmetic properties of Stern Polynomials

Autor:	Gawron, Maciej
Rok vydání:	2014
Předmět:	Mathematics - Combinatorics Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	We investigate the Stern polynomials defined by $B_0 ( t ) =0,B_1 ( t ) =1$, and for $n \geq 2$ by the recurrence relations $B_{2n}( t) =tB_{n}( t) ,$ $B_{2n+1}( t) =B_n( t) +B_{n+1}( t) $. We prove that all possible rational roots of that polynomials are $0,-1,-1/2,-1/3$. We give complete characterization of $n$ such that $deg( B_n) = deg( B_{n+1}) $ and $deg( B_n) =deg( B_{n+1}) =deg( B_{n+2}) $. Moreover, we present some result concerning reciprocal Stern polynomials. Comment: 9 pages, submitted
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1401.3553 Zobrazit plný text záznamu View this record from Arxiv