關於多項式因式函數的一個漸進公式

Abstract

我們探討一個跟古典林尼克漸近展開式很類似的有限體多項式因式函數展開式. 我們利用從多項式Brun-Titchmarsh定理得到的一些結果以及從多項式primitive character和所得的均值,使我們得到了一些結果.In this paper, we explore an analogue of the classical Linnik's asymptotic expansion about polynomial divisor functions for polynomial rings over finite fields. Our method depends on the obtained result in the polynomial Brun-Titchmarsh theorem for polynomial divisor functions and an average of polynomial primitive character sums, we obtain a polynomial Linnik's asymptotic expansion.