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函数域常值域扩张的类数整除性
On the Divisibility of Class Number in Constant Extensions of Algebraic Function Fields
设K/Fq是亏格大于0的整体函数域，Kn：=KFqn是K上的n次常值域扩张.利用整体函数域zeta函数的整系数多项式的有理表达式，结合函数域常值域扩张的基本性质，对于满足特定条件的素数l，本文讨论了使得除子类群Pic0（Kn）的Sylow-l子群为非平凡群的常值域扩张Kn的存在性.
Let K/Fq be a global function field over finite field Fq with genus greater than 0. Suppose that Kn:=KFqn is a constant field extension of K with degree n. Together the rational expression for zeta function of K with the properties of constant field extensions, for a specified prime number l, we study in this paper the existence of constant field extension Kn/K with l dividing the order of group Pic0(Kn), which is the group of divisor classes of degree zero of function field Kn.
函数域 / 除子 / 类数 {{custom_keyword}} /
function fields / divisor / class number {{custom_keyword}} /
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国家自然科学基金资助项目（11601009）；安徽省自然科学基金资助项目（1608085QA04）
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