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Integral zeros of a polynomial with linear recurrences as coefficients
Indagationes Mathematicae ( IF 0.5 ) Pub Date : 2021-03-10 , DOI: 10.1016/j.indag.2021.03.001 Clemens Fuchs , Sebastian Heintze
中文翻译:
以系数为线性递归的多项式的积分零
更新日期:2021-04-20
Indagationes Mathematicae ( IF 0.5 ) Pub Date : 2021-03-10 , DOI: 10.1016/j.indag.2021.03.001 Clemens Fuchs , Sebastian Heintze
Let be a number field, a finite set of places of , and be the ring of -integers. Moreover, let be a polynomial in having simple linear recurrences of integers evaluated at as coefficients. Assuming some technical conditions we give a description of the zeros of the above polynomial. We also give a result in the spirit of Hilbert irreducibility for such polynomials.
中文翻译:
以系数为线性递归的多项式的积分零
让 是一个数字字段, 有限的地方 , 和 成为...的戒指 -整数。而且,让是...的多项式 具有在以下位置求值的整数的简单线性递归 作为系数。假设一些技术条件,我们对零点进行描述上述多项式的 对于这种多项式,我们也秉承了希尔伯特不可约的精神,给出了一个结果。