Based on the quadratic exponential method, this paper constructs two types of generators over fi-nite field Fq , the digital quadratic exponential generator and quadratic exponential pseudorandom vector gen-erator. We...Based on the quadratic exponential method, this paper constructs two types of generators over fi-nite field Fq , the digital quadratic exponential generator and quadratic exponential pseudorandom vector gen-erator. We investigate the distribution of the sequence generated by the generators, and present results about their one dimensional discrepancy. The proofs are based on the estimate of certain character sum over Fq .If t is the least period of the sequence and t ≥ q1 /2 +2 ε,then the bound of the discrepancy is O (t ? 1/4 q1 /8+ εlog q)for any ε > 0.It shows that the sequence is asymptotically uniformly distributed.展开更多
The generic Newton polygon of L-functions associated with the exponential sums of poly- nomials of degree 3 in two variables is studied by Dwork＇s analytic methods. Wan＇s conjecture is shown to be true for this case.
利用经典高斯和的性质及解析方法研究了素数模p≡1 mod 3时的一类广义二项指数和四次均值的计算问题,并给出了其关于主特征、勒让德符号、三次特征及其他情况的计算公式。以上结果不仅完善了此类问题的研究,并对进一步研究具有很好的借...利用经典高斯和的性质及解析方法研究了素数模p≡1 mod 3时的一类广义二项指数和四次均值的计算问题,并给出了其关于主特征、勒让德符号、三次特征及其他情况的计算公式。以上结果不仅完善了此类问题的研究,并对进一步研究具有很好的借鉴作用。展开更多
基金Supported by the Special Fund of National Excellent Doctoral Dissertation (Grant 200060) and the National Natural Science Foundation of China (No.60373092).
文摘Based on the quadratic exponential method, this paper constructs two types of generators over fi-nite field Fq , the digital quadratic exponential generator and quadratic exponential pseudorandom vector gen-erator. We investigate the distribution of the sequence generated by the generators, and present results about their one dimensional discrepancy. The proofs are based on the estimate of certain character sum over Fq .If t is the least period of the sequence and t ≥ q1 /2 +2 ε,then the bound of the discrepancy is O (t ? 1/4 q1 /8+ εlog q)for any ε > 0.It shows that the sequence is asymptotically uniformly distributed.
基金Supported by National Natural Science Foundation of China (Grant No. 10671015)
文摘The generic Newton polygon of L-functions associated with the exponential sums of poly- nomials of degree 3 in two variables is studied by Dwork＇s analytic methods. Wan＇s conjecture is shown to be true for this case.
