论文标题
在常数$ d（q）$上定义的$ d（q）$
On the constant $D(q)$ defined by Homma
论文作者
论文摘要
令$ \ Mathcal {X} $为有限字段$ \ mathbb {f} _q $带有$ q $元素的投影，不可约，非字体代数曲线，让$ | \ mathcal {x}（x}（x}（\ mathbb {f} _q _q _q）| $和$ g（$ g（y Math）在过去的几十年中，ihara常数$ a（q）$已经进行了深入研究，它被定义为$ | \ m m缩的极限上级{x}（\ mathbb {f} _q）|/g（\ mathcal x）$，为$ \ m artercal x $的属。在2012年，Homma定义了$ a（q）$的类似物$ d（q）$，其中$ \ Mathcal x $的非语言被删除，$ g（\ mathcal x）$被$ \ m artercal x $替换。我们将称为$ d（q）$ homma的常数。在本文中，找到了$ d（q）$的上限和下限。
Let $\mathcal{X}$ be a projective, irreducible, nonsingular algebraic curve over the finite field $\mathbb{F}_q$ with $q$ elements and let $|\mathcal{X}(\mathbb{F}_q)|$ and $g(\mathcal X)$ be its number of rational points and genus respectively. The Ihara constant $A(q)$ has been intensively studied during the last decades, and it is defined as the limit superior of $|\mathcal{X}(\mathbb{F}_q)|/g(\mathcal X)$ as the genus of $\mathcal X$ goes to infinity. In 2012 Homma defined an analogue $D(q)$ of $A(q)$, where the nonsingularity of $\mathcal X$ is dropped and $g(\mathcal X)$ is replaced with the degree of $\mathcal X$. We will call $D(q)$ Homma's constant. In this paper, upper and lower bounds for the value of $D(q)$ are found.
