共查询到20条相似文献,搜索用时 15 毫秒
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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
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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
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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
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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
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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
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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
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ToddCOCHRANE ChunLeiLIU ZhiYongZHENG 《数学学报(英文版)》2003,19(2):327-338
We obtain formulac and estimates for character sums of the type S(x,f,p^m)=∑x=1^p^mx(f(f)),where p^m is a prime power with m≥2,x is a multiplicative character(mod p^m),and f=f1/f2 is a rational function over Z.In particular,if p is odd,d=deg(f1) deg(f2) and d^*=max(deg(f1),deg(f2)) then we obtain |S(x,f,p^m)|≤(d-1)p^m(1-1/d^*) for any non-constant f (mod p) and primitive character x.For p=2 an extra factor of 2√2 is needed. 相似文献
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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
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Wen Peng ZHANG Xiao Ying WANG 《数学学报(英文版)》2007,23(1):153-164
The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8) by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study. 相似文献
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In this paper, by using superposition method, we aim to show that ∑^n i=1 (2/- 1)^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 (2i - 1)^2k is the product of n(2n - 1)(2n + 1) and a rational polynomial in (2n - 1)(2n + 1) with degree k - 1. Moreover, recurrence formulas to compute the coefficients of the corresponding rational polynomials are also obtained. 相似文献
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An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb. 相似文献
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Henri Faure 《Monatshefte für Mathematik》2000,131(4):263-277
Let be the binomial coefficient modulo b (b prime), with if l is greater than c, and let be the sum of binomial coefficients modulo b, that is (mod b). We prove the following property: the for which the couples c, l verify and are uniformly distributed in the residue classes modulo b as n tends to infinity. The method, using the Perron-Frobenius theory, applies also to and gives a new proof of the well known result for the non-zero binomial coefficients modulo b.
(Received 21 June 1999; in revised form 13 July 2000) 相似文献
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In this paper, we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime
powers, e.g.,
for any distinct odd primes p and q. Meanwhile, we discuss the connections with the prime recognitions.
Received November 5, 1998, Accepted December 7, 2000. 相似文献
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Wenguang Zhai 《Monatshefte für Mathematik》2005,144(3):233-250
For fixed k3, let
It is known that the asymptotic formula
holds for some constant ck. Let Ek(x)=Rk(x)–ckx2/k. We cannot improve the exponent 1/k at present if we do not have further knowledge about the distribution of the zeros of the Riemann Zeta function (s). In this paper, we shall prove that if the Riemann Hypothesis (RH) is true, then Ek(x)=O(x4/15+), which improves the earlier exponent 5/18 due to Nowak. A mean square estimate of Ek(x) for k6 is also obtained, which implies that Ek(x)=(x1/k–1/k2) for k6 under RH. 相似文献
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The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given. 相似文献