共查询到20条相似文献,搜索用时 15 毫秒
1.
Chunlei Liu 《数学学报(英文版)》2000,16(3):535-540
Abstract
Hua’s estimate is established for character sums in a number field. A relationship between liftings of a character sum in
a local field is also studied.
This work is supported by NNSFC 相似文献
2.
3.
Nicholas M. Katz 《Geometric And Functional Analysis》2008,18(4):1251-1269
We give sharp estimates for certain families of exponential sums in several variables over finite fields.
Received: May 2007, Accepted: September 2007 相似文献
4.
The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums,and give several interesting identities and asymptotic formulae for them. 相似文献
5.
Sums of Five Almost Equal Prime Squares 总被引:5,自引:0,他引:5
Claus BAUER 《数学学报(英文版)》2005,21(4):833-840
Let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 (mod 24) can be written as N=p1^2+p2^2+P3^2+p4^2 +p5^2, where │√N5-Pi│≤N^1/2-19/850+∈. 相似文献
6.
Miriam Cohen 《代数通讯》2013,41(12):4618-4633
We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS 3), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums. 相似文献
7.
We show that for any mod 2m characters, χ1, χ2, the complete exponential sum,∑~(2m)_(x=1)χ1(x)χ2(Ax~k+ B) has a simple explicit evaluation. 相似文献
8.
两项指数和及两项特征和的混合均值 总被引:1,自引:0,他引:1
利用解析方法以及高斯和的性质研究一类二项指数和及二项特征和的混合均值问题,并给出一个精确的表示式.作为应用,给出该和式的一个渐近公式以及该和式与Dirichlet L-函数加权均值的一个较强的渐近公式. 相似文献
9.
In the usual construction of non-holomorphic Eisenstein series, for a general Fuchsian group, a multiplicative character may be included. The properties of these series are well known. Here we instead include an additive character and develop the properties of the resulting series. We pay particular attention to additive characters that are non-cuspidal, i.e., that are not zero on some parabolic generators. These series may be used to estimate certain additive character sums. For example, asymptotics for a weighted sum over group elements that counts the number of appearances of a fixed generator of the Fuchsian group are obtained. 相似文献
10.
Zai Zhao MENG 《数学学报(英文版)》2006,22(2):561-570
We use the resultant of two polynomials to discuss the roots of congruences, and then we improve the result of Burgess on the mean values of character sums in the case r = 3. Finally, we give a new estimate for the mean values of character sums in the case r = 4. 相似文献
11.
本文利用三角和估计及其特征和的性质研究一类二项指数和与多项式特征和的混合均值的计算问题,并给出两个有趣的计算公式. 相似文献
12.
本文主要利用解析方法以及二项指数和与Dirichlet特征的性质,研究多项式的特征和与二项三次指数和的混合均值的计算问题,并得到一个较强的渐近公式. 相似文献
13.
For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is a π-separable group,we show that the sum of the entries in the table of Isaacs' partial characters is a real number,and we obtain upper and lower bounds for this sum. 相似文献
14.
The main purpose of this paper is using the analytic method and the properties of trigonometric sums and character sums to study the computational problem of one kind hybrid power mean involving two-term exponential sums and polynomial character sums. Then the authors give some interesting calculating formulae for them. 相似文献
15.
F. Chamizo 《Journal of Mathematical Analysis and Applications》2009,350(1):283-289
We combine exponential sums, character sums and Fourier coefficients of automorphic forms to improve the best known upper bound for the lattice error term associated to rational ellipsoids. 相似文献
16.
Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results. 相似文献
17.
A Van der Corput exponential sum is S = exp (2 i f(m)) wherem has size M, the function f(x) has size T and = (log M) / log T < 1. There are different bounds for S in differentranges for . In the middle range where is near 1/over 2, . This bounds the exponent of growthof the Riemann zeta function on its critical line Re s = 1/over2. Van der Corput used an iteration which changed at each step.The BombieriIwaniec method, whilst still based on meansquares, introduces number-theoretic ideas and problems. TheSecond Spacing Problem is to count the number of resonancesbetween short intervals of the sum, when two arcs of the graphof y = f'(x) coincide approximately after an automorphism ofthe integer lattice. In the previous paper in this series [Proc.London Math. Soc. (3) 66 (1993) 140] and the monographArea, lattice points, and exponential sums we saw that coincidenceimplies that there is an integer point close to some resonancecurve, one of a family of curves in some dual space,now calculated accurately in the paper Resonance curvesin the BombieriIwaniec method, which is to appearin Funct. Approx. Comment. Math. We turn the whole BombieriIwaniec method into an axiomatisedstep: an upper bound for the number of integer points closeto a plane curve gives a bound in the Second Spacing Problem,and a small improvement in the bound for S. Ends and cusps ofresonance curves are treated separately. Bounds for sums oftype S lead to bounds for integer points close to curves, andanother branching iteration. Luckily Swinnerton-Dyer's methodis stronger. We improve from 0.156140... in the previous paperand monograph to 0.156098.... In fact (32/205 + , 269/410 +) is an exponent pair for every > 0. 2000 Mathematics SubjectClassification 11L07 (primary), 11M06, 11P21, 11J54 (secondary). 相似文献
18.
Arne Winterhof 《Designs, Codes and Cryptography》2001,22(2):123-131
The results in Winterhof(On the distribution of powers in finite fields, Finite Fieldsand Their Applications 4 (1998), 43–54) on incomplete charactersums of linear polynomials are extended to incomplete charactersums of arbitrary polynomials. As applications a constructionmethod for difference matrices is given, and the estimate ofthe maximum running digital sums of some dc-constrained codesis slightly improved. 相似文献
19.
本文使用解析方法及特征和的性质研究了一类多项式的特征和与模p的狄利克莱L-函数的混合幂均值的计算问题,并给出了它们的一些计算公式. 相似文献
20.
In this paper, the authors use the analytic methods and the properties of
character sums mod p to study the computational problem of one kind of mean value
involving the classical Dedekind sums and two-term exponential sums, and give an exact
computational formula for it. 相似文献