共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank.
Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =
1/45(26n3 -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n2 + 1, and the class number of quadratic number field K2 = Q(vq) is 1. 相似文献
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In this paper,we use the analytic methods to study the mean value properties involving the classical Dedekind sums and two-term exponential sums,and give two sharper asymptotic formulae for it. 相似文献
4.
In this paper, we use the elementary and analytic methods to study the computational problem of one kind mean value involving
the classical Dedekind sums and two-term exponential sums, and give two exact computational formulae for them. 相似文献
5.
We construct some multiple Dedekind sums and relate them to the relative class number of an imaginary abelian number field. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value
problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for
it. 相似文献
7.
Emmanuel Tollis. 《Mathematics of Computation》1997,66(219):1295-1321
In this paper, we describe a computation which established the GRH to height (resp. ) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing's criterion to prove that there is no zero off the critical line. We finally give results concerning the GRH for cubic and quartic fields, tables of low zeros for number fields of degree and , and statistics about the smallest zero of a number field.
8.
Let {K
m
}
m ≥ 4 be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomial f
m
(x) = x
3 − mx
2 − (m + 1)x − 1, where m is an integer with m ≥ 4. In this paper, we will apply Siegel’s formula for the values of the zeta function of a totally real algebraic number
field at negative odd integers to K
m
, and compute the values of the Dedekind zeta function of K
m
.
This work was supported by grant No.R01-2006-000-11176-0 from the Basic Research Program of KOSEF. 相似文献
9.
We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums, and give an interesting identity and asymptotic formula for it. 相似文献
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Summary Our purpose is to extend results due to P. Chandra and L. Leindler concerning the order of approximation by means of Fourier series for functions belonging to generalized Lipschitz-classes. 相似文献
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关于广义Dedekind和的加权均值 总被引:1,自引:0,他引:1
任刚练 《纯粹数学与应用数学》2003,19(1):22-24
利用Dirichlet L-函数的均值定理和特征和估计,研究了广义Dedekind和与HurwitzZeta-函数的加权均值分布性质,并给出一个有趣的渐近公式。 相似文献
14.
Kaori Ota 《Journal of Number Theory》2003,98(2):280-309
In this paper derivatives of Dedekind sums are defined, and their reciprocity laws are proved. They are obtained from values at non-positive integers of the first derivatives of Barnes’ double zeta functions. As special cases, they give finite product expressions of the Stirling modular form and the double gamma function at positive rational numbers. 相似文献
15.
Shinji Fukuhara Noriko Yui 《Transactions of the American Mathematical Society》2004,356(10):4237-4254
We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter having positive imaginary part. When , these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable . We obtain a reciprocity law for these sums, which gives rise to new relations between certain modular forms (of one variable).
16.
本文利用正整数模q的正则数的定义以及解析方法研究一类与Dedekind和有关的和式的计算问题,并给出这个和式在一些特殊点上有趣的恒等式. 相似文献
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18.
Kok Seng Chua. 《Mathematics of Computation》2005,74(251):1457-1470
Let be a primitive, real and even Dirichlet character with conductor , and let be a positive real number. An old result of H. Davenport is that the cycle sums are all positive at and this has the immediate important consequence of the positivity of . We extend Davenport's idea to show that in fact for , 0$"> for all with so that one can deduce the positivity of by the nonnegativity of a finite sum for any . A simple algorithm then allows us to prove numerically that has no positive real zero for a conductor up to 200,000, extending the previous record of 986 due to Rosser more than 50 years ago. We also derive various estimates explicit in of the as well as the shifted cycle sums considered previously by Leu and Li for . These explicit estimates are all rather tight and may have independent interests.
19.
Erdos and Szemerédi conjectured that if is a set of positive integers, then there must be at least integers that can be written as the sum or product of two elements of . Erdos and Szemerédi proved that this number must be at least for some and . In this paper it is proved that the result holds for .
20.
Yong-Gao Chen 《Proceedings of the American Mathematical Society》1999,127(7):1927-1933
Erdös and Szemerédi proved that if is a set of positive integers, then there must be at least integers that can be written as the sum or product of two elements of , where is a constant and . Nathanson proved that the result holds for . In this paper it is proved that the result holds for and .