共查询到20条相似文献,搜索用时 15 毫秒
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Paul Thomas Young 《Journal of Number Theory》2004,106(1):13-25
Consider a Gauss sum for a finite field of characteristic p, where p is an odd prime. When such a sum (or a product of such sums) is a p-adic integer we show how it can be realized as a p-adic limit of a sequence of multinomial coefficients. As an application we generalize some congruences of Hahn and Lee to exhibit p-adic limit formulae, in terms of multinomial coefficients, for certain algebraic integers in imaginary quadratic fields related to the splitting of rational primes. We also give an example illustrating how such congruences arise from a p-integral formal group law attached to the p-adic unit part of a product of Gauss sums. 相似文献
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Ronald Evans 《Journal of Mathematical Analysis and Applications》2003,281(2):454-476
We consider the classical incomplete higher-order Gauss sums
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Brian J. Murray 《Journal of Number Theory》2007,126(1):87-109
H. Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes. 相似文献
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Jan Denef Franç ois Loeser 《Transactions of the American Mathematical Society》1998,350(12):5047-5066
The main result of this paper is a character sum identity for Coxeter arrangements over finite fields which is an analogue of Macdonald's conjecture proved by Opdam.
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The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic methods and algebraic geometric methods. We prove two conjectures which were proposed recently by the above authors in a previous article (2022). Here we obtain an asymptotic formula for arbitrary power means of generalized quadratic Gauss sums and one corresponding power moment of a character sum. 相似文献
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三次高斯和与Kloosterman和的线性递推公式 总被引:2,自引:1,他引:1
应用三角和方法以及高斯和的若干性质,研究三次高斯和与Kloosterman和的一类高次混合均值的计算问题,本文给出该混合均值的一个有趣的线性递推公式.同时,还应用该递推公式,得到三次高斯和与Kloosterman和的高次混合均值的一系列较强的渐近公式. 相似文献
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The k-subset sum problem over finite fields is a classical NP-complete problem. Motivated by coding theory applications, a more complex problem is the higher m-th moment k-subset sum problem over finite fields. We show that there is a deterministic polynomial time algorithm for the m-th moment k-subset sum problem over finite fields for each fixed m when the evaluation set is the image set of a monomial or Dickson polynomial of any degree n. In the classical case , this recovers previous results of Nguyen-Wang (the case ) [22] and the results of Choe-Choe (the case ) [3]. 相似文献
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We use a new argument to improve the error term in the asymptotic formula for the number of Diophantine m-tuples in finite fields, which is due to A. Dujella and M. Kazalicki (2021) and N. Mani and S. Rubinstein-Salzedo (2021). 相似文献
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Simon R. Blackburn 《Discrete Mathematics》2006,306(12):1126-1131
We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings. 相似文献
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In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic(continuous) functions is developed based on Dirichlet characters, Gauss sums and the generalized M¨obius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given. 相似文献
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Let be the number of solutions of the equation over the finite field , and let be the number of solutions of the equation . If , let be the least integer represented by . and play important roles in estimating . Based on a partition of , we obtain the factorizations of and , respectively. All these factorizations can simplify the corresponding calculations in most cases or give the explicit formulae for in some special cases.
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设f是有限域Fq上的n元m项多项式,D_f∈Z_(≥0)~(n×m)为其次数矩阵,用N(f)表示由超曲面f=0在仿射空间An(Fq)确定的Fq-有理点的个数.若矩阵A∈Z~(n×m)在环Z/(q-1)Z中与Df行等价,则记为D_fr~A.本文利用高斯和给出了当m≤n且0D_fr~diag(λ_1,···,λ_m),其中λi∈{1,3}时N(f)的具体表达式,从而推广了已知结论. 相似文献
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The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q (a positive odd number), and give an exact computational formula for it. 相似文献
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Andreas Aabrandt 《International Journal of Mathematical Education in Science & Technology》2016,47(6):987-991
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom. 相似文献
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We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields. Certain basic notions in finite field theory have interpretations in terms of standard graph properties. We show that the graphs are connected and provide an estimate of their diameter. An accidental graph isomorphism is uncovered and proved. The smallest non-trivial Laplace eigenvalue is given some attention, in particular for a specific family of 8-regular graphs showing that it is not an expander. We introduce a regular covering graph and show that it is connected if and only if the root is primitive. 相似文献