共查询到20条相似文献,搜索用时 15 毫秒
1.
Yilmaz Simsek 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e377
The aim of this paper is to define new generating functions. By applying a derivative operator and the Mellin transformation to these generating functions, we define q-analogue of the Genocchi zeta function, q-analogue Hurwitz type Genocchi zeta function, and q-Genocchi type l-function. We define partial zeta function. By using this function, we construct p-adic interpolation functions which interpolate generalized q-Genocchi numbers at negative integers. We also define p-adic meromorphic functions on Cp. Furthermore, we construct new generating functions of q-Hardy-Berndt type sums and q-Hardy-Berndt type sums attached to Dirichlet character. We also give some new relations, related to these sums. 相似文献
2.
Yilmaz Simsek 《Journal of Mathematical Analysis and Applications》2006,318(1):333-351
The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well. 相似文献
3.
We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity. 相似文献
4.
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, ln (q) and ln sin(q). 相似文献
5.
Nobushige Kurokawa Katsuhisa Mimachi Masato Wakayama 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):43-56
We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from
the one relating to the Hurwitz zeta function.
Partially supported by Grant-in-Aid for Exploratory Research No. 15654003.
Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340003.
Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012. 相似文献
6.
Yoshihiro Takeyama 《The Ramanujan Journal》2012,27(1):15-28
We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV’s). In the limit q→1, it turns into Kawashima’s relation for multiple zeta values. As a corollary we find that qMZV’s satisfy the linear relation contained in Kawashima’s relation. In the proof we make use of a q-analogue of Newton series and Bradley’s duality formula for finite multiple harmonic q-series. 相似文献
7.
Junesang Choi P.J. Anderson H.M. Srivastava 《Applied mathematics and computation》2009,215(3):1185-1208
In this paper, we systematically recover the identities for the q-eta numbers ηk and the q-eta polynomials ηk(x), presented by Carlitz [L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948) 987–1000], which we define here via generating series rather than via the difference equations of Carlitz. Following a method developed by Kaneko et al. [M. Kaneko, N. Kurokawa, M. Wakayama, A variation of Euler’s approach to the Riemann zeta function, Kyushu J. Math. 57 (2003) 175–192] for a canonical q-extension of the Riemann zeta function, we investigate a similarly constructed q-extension of the Hurwitz zeta function. The details of this investigation disclose some interesting connections among q-eta polynomials, Carlitz’s q-Bernoulli polynomials -polynomials, and the q-Bernoulli polynomials that emerge from the q-extension of the Hurwitz zeta function discussed here. 相似文献
8.
Taekyun Kim 《Journal of Number Theory》2009,129(7):1798-1804
We consider the q-analogue of the Euler zeta function which is defined by
9.
Nobushige Kurokawa Katsuhisa Mimachi Masato Wakayama 《Rendiconti del Circolo Matematico di Palermo》1932,56(1):43-56
We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function. 相似文献
10.
Wadim Zudilin 《manuscripta mathematica》2002,107(4):463-477
We sharpen the known irrationality measures for the quantities , where z ? {±1} and p ?ℤ \ {0, ±1}. Our construction of auxiliary linear forms gives a q-analogue of the approach recently applied to irrationality problems for the values of the Riemann zeta function at positive
integers. We also present a method for improving estimates of the irrationality measures of q-series.
Received: 22 October 2001 相似文献
11.
Jasper V. Stokman 《Journal of Approximation Theory》2002,114(2):308-342
The Askey–Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the Askey–Wilson second order q-difference operator. The kernel is called the Askey–Wilson function. In this paper an explicit expansion formula for the Askey–Wilson function in terms of Askey–Wilson polynomials is proven. With this expansion formula at hand, the image under the Askey–Wilson function transform of an Askey–Wilson polynomial multiplied by an analogue of the Gaussian is computed explicitly. As a special case of these formulas a q-analogue (in one variable) of the Macdonald–Mehta integral is obtained, for which also two alternative, direct proofs are presented. 相似文献
12.
In this paper we establish a q-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime. 相似文献
13.
Yves Aubry 《Journal of Number Theory》2008,128(7):2053-2062
We show that, for any finite field Fq, there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial. 相似文献
14.
Hidehiko Mishou 《Archiv der Mathematik》2008,90(3):230-238
In the previous paper [9] the author proved the joint limit theorem for the Riemann zeta function and the Hurwitz zeta function
attached with a transcendental real number. As a corollary, the author obtained the joint functional independence for these
two zeta functions. In this paper, we study the joint value distribution for the Riemann zeta function and the Hurwitz zeta
function attached with an algebraic irrational number. Especially we establish the weak joint functional independence for
these two zeta functions.
Received: 17 Apri1 2007 相似文献
15.
Sheng Chen 《Linear algebra and its applications》2009,431(8):1397-1406
In this paper the relation between the zeta function of an integral matrix and its generalized Bowen-Franks groups is studied. Suppose that A and B are nonnegative integral matrices whose invertible part is diagonalizable over the field of complex numbers and A and B have the same zeta function. Then there is an integer m, which depends only on the zeta function, such that, for any prime q such that gcd(q,m)=1, for any g(x)∈Z[x] with g(0)=1, the q-Sylow subgroup of the generalized Bowen-Franks group BFg(x)(A) and BFg(x)(B) are the same. In particular, if m=1, then zeta function determines generalized Bowen-Franks groups. 相似文献
16.
We prove a new relation for the multiple q-zeta values (MqZV’s). It is a q-analogue of the Ohno-Zagier relation for the multiple zeta values (MZV’s). We discuss the problem of determining the dimension
of the space spanned by MqZV’s over ℚ, and present an application to MZV.
The first author is supported by Grant-in-Aid for Young Scientists (B) No. 17740026 and the second author is supported by
Grant-in-Aid for Young Scientists (B) No. 17740089. 相似文献
17.
We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(q), ln (q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions A
k(q) := k(1 – k, q), k
, and a family of polygamma functions of negative order, whose properties we study in some detail. 相似文献
18.
We provide an explicit formula for the Tornheim double series T(a,0,c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a=m, c=n, we show that in the most interesting case of even weight N:=m+n the Tornheim sum T(m,0,n) can be expressed in terms of zeta values and the family of integrals
ò01logG(q)Bk(q)\operatornameCll+1(2pq) dq,\int_{0}^{1}\log\Gamma(q)B_{k}(q)\operatorname{Cl}_{l+1}(2\pi q)\,dq,\vspace*{-3pt} 相似文献
19.
Linas Vepštas 《Numerical Algorithms》2008,47(3):211-252
This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies
this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function. As such, it may be taken as an extension
of the techniques given by Borwein’s “An efficient algorithm for computing the Riemann zeta function” by Borwein for computing
the Riemann zeta function, to more general series. The algorithm provides a rapid means of evaluating Li
s
(z) for general values of complex s and a kidney-shaped region of complex z values given by ∣z
2/(z–1)∣<4. By using the duplication formula and the inversion formula, the range of convergence for the polylogarithm may be
extended to the entire complex z-plane, and so the algorithms described here allow for the evaluation of the polylogarithm for all complex s and z values. Alternatively, the Hurwitz zeta can be very rapidly evaluated by means of an Euler–Maclaurin series. The polylogarithm
and the Hurwitz zeta are related, in that two evaluations of the one can be used to obtain a value of the other; thus, either
algorithm can be used to evaluate either function. The Euler–Maclaurin series is a clear performance winner for the Hurwitz
zeta, while the Borwein algorithm is superior for evaluating the polylogarithm in the kidney-shaped region. Both algorithms
are superior to the simple Taylor’s series or direct summation. The primary, concrete result of this paper is an algorithm
allows the exploration of the Hurwitz zeta in the critical strip, where fast algorithms are otherwise unavailable. A discussion
of the monodromy group of the polylogarithm is included.
相似文献
20.
We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Díaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma distribution. 相似文献
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