关键词: 指数和, 迹函数, 二次函数, 多项式分解

Abstract: Factorizing the companion polynomials of binary quadratic function into the product of a polynomial and its reciprocal polynomial. With the property of the trace function and the Frobenius permutation, the exponential sums of a large class of quadratic functions with many terms can be converted to the computation of the exponential sums of some quadratic functions that can be explicitly evaluated by present results. A new method is also given to simplify the evaluation of exponential sums of these binary quadratic functions.

Key words: exponential sums, trace function, quadratic functions, the factorization of polynomial