Let \({\mathbb {F}}_{q}\) be the finite field of q elements and \(\chi _{1},\ldots ,\chi _{n}\) the multiplicative characters of \({\mathbb {F}}_{q}\). Given a Laurent polynomial \(f(X)\in {\mathbb {F}}_q[x_1^{\pm 1},\dots ,x_n^{\pm 1}]\), the corresponding L-function is defined to be

where \(S^{*}_{h}(\chi _{1},\ldots ,\chi _{n},f)\) is the twisted exponential sum defined in the extension of \({\mathbb {F}}_{q}\) of degree h. In this paper, we obtain the explicit formulae for \(L^{*}(\chi _{1},\ldots ,\chi _{n},f;T)\) for the Laurent polynomials with full column rank exponent matrix in terms of p-adic gamma functions, which generalizes the results of Wan, Hong and Cao. We also evaluate the slopes of the reciprocal zeros and reciprocal poles of \(L^{*}(\chi _{1},\ldots ,\chi _{n},f;T)\) and determine the p-adic Newton polygons of the polynomials associated to the L-function \(L^{*}(\chi _{1},\ldots ,\chi _{n},f;T)\).

令\（{\ mathbb {F}} _ {q} \）为q个元素的有限域，而\（\ chi _ {1}，\ ldots，\ chi _ {n} \）为\（（ {\ mathbb {F}} _ {q} \）。给定Laurent多项式\ {f（X）\ in {\ mathbb {F}} _ q [x_1 ^ {\ pm 1}，\ dots，x_n ^ {\ pm 1}] \）中，定义了相应的L函数成为

其中\（S ^ {** __ h}（\ chi _ {1}，\ ldots，\ chi _ {n}，f）\）是\（{\ mathbb { F}} _ {q} \）程度的ħ。在本文中，我们获得了具有完整列秩指数的Laurent多项式\（L ^ {*}（\ chi _ {1}，\ ldots，\ chi _ {n}，f; T）\）的显式公式用p -adic伽玛函数表示的矩阵，概括了Wan，Hong和Cao的结果。我们还评估\（L ^ {*}（\ chi _ {1}，\ ldots，\ chi _ {n}，f; T）\）的倒数零和倒数极点的斜率并确定p -adic与L函数\（L ^ {*}（\ chi _ {1}，\ ldots，\ chi _ {n}，f; T）\）相关的多项式的牛顿多边形。