L-functions of twisted exponential sums over finite fields
L-functions of twisted exponential sums over finite fields
复制标题
有限域上扭曲指数和的 L 函数
DOI：
10.1007/s11139-019-00230-4
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发表时间：
2020
影响因子：
0.7
通讯作者：
Hong Shaofang
中科院分区：
文献类型：
--
作者：
Cao Wei;Hong Shaofang
Letbe the finite field ofqelements andthe multiplicative characters of. Given a Laurent polynomial, the corresponding L-function is defined to be $$\begin{aligned} L^{*}(\chi _{1},\ldots ,\chi _{n},f;T) =\exp \Big (\sum \nolimits _{h=1}^{\infty }S^{*}_{h}(\chi _{1},\ldots ,\chi _{n},f)\frac{T^{h}}{h}\Big ), \end{aligned}$$whereis the twisted exponential sum defined in the extension ofof degreeh. In this paper, we obtain the explicit formulae forfor the Laurent polynomials with full column rank exponent matrix in terms ofp-adic gamma functions, which generalizes the results of Wan, Hong and Cao. We also evaluate the slopes of the reciprocal zeros and reciprocal poles ofand determine thep-adic Newton polygons of the polynomials associated to the L-function.
Letbe the finite field ofqelements andthe multiplicative characters of. Given a Laurent polynomial, the corresponding L-function is defined to be $$\begin{aligned} L^{*}(\chi _{1},\ldots ,\chi _{n},f;T) =\exp \Big (\sum \nolimits _{h=1}^{\infty }S^{*}_{h}(\chi _{1},\ldots ,\chi _{n},f)\frac{T^{h}}{h}\Big ), \end{aligned}$$whereis the twisted exponential sum defined in the extension ofof degreeh. In this paper, we obtain the explicit formulae forfor the Laurent polynomials with full column rank exponent matrix in terms ofp-adic gamma functions, which generalizes the results of Wan, Hong and Cao. We also evaluate the slopes of the reciprocal zeros and reciprocal poles ofand determine thep-adic Newton polygons of the polynomials associated to the L-function.