论文标题
分解功能字段中指数和对数系数
Factorization of Coefficients for Exponential and Logarithm in Function Fields
论文作者
论文摘要
令$ x $为椭圆曲线或超过$ \ mathbb f_q $的损坏的过纤维曲线。我们将讨论如何在此类曲线上为Hayes模块分解指数和对数系列的系数。这使我们能够为$ v $ -ADIC收敛结果，以$ v $ a“有限”素数为指数和对数系列。作为一个应用程序，我们可以证明$ v $ -ADIC GOSS $ L $ -VALUE $ L_V（1，ψ）$是合适的字符$ψ$的log-algebraic。
Let $X$ be an elliptic curve or a ramifying hyperelliptic curve over $\mathbb F_q$. We will discuss how to factorize the coefficients of the exponential and logarithm series for a Hayes module over such a curve. This allows us to obtain $v$-adic convergence results for such exponential and logarithm series, for $v$ a 'finite' prime. As an application, we can show that the $v$-adic Goss $L$-value $L_v(1, Ψ)$ is log-algebraic for suitable characters $Ψ$.
