共查询到20条相似文献,搜索用时 15 毫秒
1.
Let be a non-normal cubic extension over Q.We study the higher moment of the coefficients aK3(n)of Dedckind zeta function over sum of two squares∑n21+n22≤xa1K3(n21+n22),where 2≤l≤8 and n1,n2,l∈Z. 相似文献
2.
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.
3.
Guangshi Lü 《Journal of Number Theory》2011,131(10):1924-1938
In this paper, we are interested in the average behavior of the coefficients of Dedekind zeta function over square numbers. In Galois fields of degree d which is odd, when l?1 is an integer, we have
4.
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
5.
J. M. B. Noronha 《Integral Transforms and Special Functions》2017,28(6):423-442
We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an integral representation for the finite parts at the poles. Similar results are derived for an associated function, which we term homogeneous Barnes zeta function. Our expressions immediately yield analogous representations for the logarithm of the Barnes gamma function, including the particular case also known as multiple gamma function. 相似文献
6.
Necdet Batir 《Proceedings Mathematical Sciences》2008,118(4):495-503
We establish various new inequalities for the Hurwitz zeta function. Our results generalize some known results for the polygamma
functions to the Hurwitz zeta function. 相似文献
7.
H. Mishou 《Lithuanian Mathematical Journal》2007,47(1):32-47
In this paper, we investigate the joint value-distribution for the Riemann zeta function and Hurwitz zeta function attached
with a transcendental real parameter. Especially, we establish the joint universality theorem for these two zeta functions.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 1, pp. 39–57, January–March, 2007. 相似文献
8.
A. Connes 《Selecta Mathematica, New Series》1999,5(1):29-106
We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual
noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a
trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace
formula and eliminates the parameter of our previous approach. 相似文献
9.
Each simple zero of the Riemann zeta function on the critical line with is a center for the flow of the Riemann xi function with an associated period . It is shown that, as , Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture for some exponent , we obtain the upper bound . Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, . Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert-Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis.
10.
Djurdje Cvijovi? 《Applied mathematics and computation》2012,218(12):6744-6747
It is demonstrated that the alternating Lipschitz-Lerch zeta function and the alternating Hurwitz zeta function constitute a discrete Fourier transform pair. This discrete transform pair makes it possible to deduce, as special cases and consequences, many (mainly new) transformation relations involving the values at rational arguments of alternating variants of various zeta functions, such as the Lerch and Hurwitz zeta functions and Legendre chi function. 相似文献
11.
12.
Let ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have
(1-δ(x))ζ(x)+αδ(x)<ζ(x+1)<(1-δ(x))ζ(x)+βδ(x),