函数域上双重酉除数函数的均值  

The Average Value of Bi-Unitary Divisor Function in Function Fields

作　　者：马顺琪 

机构地区：[1]青岛大学数学与统计学院,山东 青岛

出　　处：《理论数学》2021年第10期1712-1719,共8页Pure Mathematics

摘　　要：设Fq为q元有限域,在函数域Fq(T)中,我们称首一多项式d为多项式f的酉因式,如果f=dδ且(d,δ)=1。若d同时为多项式f与g的酉因式,则称d是f与g的酉公因式。记(f,g)∗∗为f与g的次数最大的首一酉公因式。我们称g是f的双重酉因式,如果f=gh且(g,h)∗∗=1。令τ∗∗(f)为f的双重酉因式的个数,本文研究了τ∗∗(f)的均值,并给出了相应的渐近公式。Let Fq be the finite field with q elements. In the function field Fq(T), a monic divisor d of a polynomial f is called unitary, if f=dδ and (d,δ)=1. For polynomials f,g, if d is an unitary divisor of both f and g, it is called the common unitary divisor of them. Let (f,g)∗∗ be the common unitary monic divisor of f and g, whose degree is the largest. We say a divisor g of f is bi-unitary, if f=gh and (g,h)∗∗=1. Let τ∗∗(f) denote the number of bi-unitary divisor of f. We consider the average value of τ∗∗(f) and give a corresponding asymptotic formula.

关 键 词：双重酉除数函数 函数域 均值 

分 类 号：O15[理学—数学]