Acta Scientiarum Naturalium Universitatis Pekinensis

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Simplifying the Evaluation of Exponential Sums of Some Binary Quadratic Functions

YIN Huajun, ZHANG Xiyong   

  1. Department of Applied Mathematics, School of Institute of Information Engineering, Information Engineering University, Zhengzhou 450002;
  • Received:2011-11-15 Online:2012-09-20 Published:2012-09-20

一类二次函数指数和的简化计算

尹华军,张习勇   

  1. 信息工程大学信息工程学院应用数学系, 郑州 450002;

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

摘要: 利用二次函数伴随多项式的一种特定分解形式, 结合Frobenius变换和有限域上迹函数的性质, 将一类二次函数的指数和转化为目前可计算的形式。并给出一种简化二次函数指数和计算的新方法。

关键词: 指数和, 迹函数, 二次函数, 多项式分解

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