共查询到20条相似文献,搜索用时 15 毫秒
1.
Taekyun Kim 《Journal of Mathematical Analysis and Applications》2007,329(2):1472-1481
In this paper, we give an explicit p-adic expansion of
2.
Tim Huber 《Journal of Combinatorial Theory, Series A》2010,117(4):361-2622
New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan's Lost Notebook. The results presented here are, in part, a response to a conjecture made by M.E.H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of the Rogers-Ramanujan series. Related generating functions appear in the work of H. Prodinger and L.L. Cristea in their study of geometrically distributed random variables. An elementary combinatorial interpretation for each of these enumerating functions is given in terms of a related set of statistics. 相似文献
3.
One of the purposes of this paper is to construct the twisted q-Euler numbers by using p-adic invariant integral on Zp in the fermionic sense. Moreover, we consider the twisted Euler q-zeta functions and q-l-functions which interpolate the twisted q-Euler numbers and polynomials at a negative integer. 相似文献
4.
Brett A. Tangedal 《Journal of Number Theory》2011,131(7):1240-1257
Text
We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. We conclude with a Laurent series expansion of the p-adic multiple log gamma function for (p-adically) large x which agrees exactly with Barnes?s asymptotic expansion for the (complex) multiple log gamma function, with the fortunate exception that the error term vanishes. Indeed, it was the possibility of such an expansion which served as the motivation for our functions, since we can use these expansions computationally to p-adically investigate conjectures of Gross, Kashio, and Yoshida over totally real number fields.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=I9Bv_CycEd8. 相似文献5.
Qiu-Ming Luo 《Journal of Mathematical Analysis and Applications》2010,363(1):7-18
We show some results for the q-Bernoulli and q-Euler polynomials. The formulas in series of the Carlitz's q-Stirling numbers of the second kind are also considered. The q-analogues of well-known formulas are derived from these results. 相似文献
6.
Yilmaz Simsek 《Applied mathematics and computation》2010,216(10):2976-973
The main purpose of this paper is to construct a family of modified p-adic twisted functions, which interpolate the modified twisted q-Bernoulli polynomials and the generalized twisted q-Bernoulli numbers at negative integers. We also give some applications and examples related to these functions and numbers. 相似文献
7.
Kumi Yasuda 《Journal of Functional Analysis》2004,216(2):422-454
This article aims at showing a p-adic analogue of Selberg's trace formula, which describes a duality between the spectrum of a Hilbert-Schmidt operator and the length of prime geodesics appearing in the p-adic upper half-plane associated with a hyperbolic discontinuous subgroup of . Then we construct Markov processes on the fundamental domain relative to such subgroups, to whose transition operators the trace formula applied and a p-adic analogue of prime geodesic theorem is proved. 相似文献
8.
A.Yu. Khrennikov 《Journal of Mathematical Analysis and Applications》2009,350(1):170-183
We study the asymptotical behavior of the p-adic singular Fourier integrals
9.
Raf Cluckers 《Journal of Number Theory》2008,128(7):2185-2197
In [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114], it is shown that a p-adic semi-algebraic set can be partitioned in such a way that each part is semi-algebraically isomorphic to a Cartesian product where the sets R(k) are very basic subsets of Qp. It is suggested in [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114] that this result can be adapted to become useful to p-adic integration theory, by controlling the Jacobians of the occurring isomorphisms. In this paper we show that the isomorphisms can be chosen in such a way that the valuations of their Jacobians equal the valuations of products of coordinate functions, hence obtaining a kind of explicit p-adic resolution of singularities for semi-algebraic p-adic functions. We do this by restricting the used isomorphisms to a few specific types of functions, and by controlling the order in which they appear. This leads to an alternative proof of the rationality of the Poincaré series associated to the p-adic points on a variety, as proven by Denef in [J. Denef, The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math. 77 (1984) 1-23]. 相似文献
10.
We solve the Cauchy problems for p-adic linear and semi-linear evolutionary pseudo-differential equations (the time-variable t∈R and the space-variable ). Among the equations under consideration there are the heat type equation and the Schrödinger type equations (linear and nonlinear). To solve these problems, we develop the “variable separation method” (an analog of the classical Fourier method) which reduces solving evolutionary pseudo-differential equations to solving ordinary differential equations with respect to real variable t. The problem of stabilization for solutions of the Cauchy problems as t→∞ is also studied. These results give significant advance in the theory of p-adic pseudo-differential equations and can be used in applications. 相似文献
11.
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
12.
Amnon Besser 《Journal of Number Theory》2005,111(2):318-371
We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the metric on the determinant of its cohomology in the style of Faltings. We also prove analogues of the Adjunction formula and the Riemann-Roch formula. 相似文献
13.
X.-F. Roblot 《Journal of Number Theory》2004,107(1):168-206
In a previous paper (Ann. L’ Inst. Fourier 52(2) (2002) 379-417) the second-named author developed a new approach to the abelian p-adic Stark conjecture at s=1 and stated some related conjectures. The aim of the present paper is to develop and apply techniques to numerically investigate one of these—the ‘Weak Refined Combined Conjecture’—in 15 cases. 相似文献
14.
Kyung Soo Rim 《Journal of Mathematical Analysis and Applications》2006,324(2):1470-1477
In the p-adic vector space , we characterize those non-negative functions ψ defined on for which the weighted Hardy-Littlewood average is bounded on (1?r?∞), and on . Also, in each case, we find the corresponding operator norm ‖Uψ‖. 相似文献
15.
In this work we present a derivation for the complete asymptotic expansions of Euler?s q-exponential function and Jackson?s q-gamma function via Mellin transform. These formulas are valid everywhere, uniformly on any compact subset of the complex plane. 相似文献
16.
Taekyun Kim 《Journal of Mathematical Analysis and Applications》2002,273(1):236-242
The purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli numbers of higher order, which is an answer to a part of the problem in a previous publication (see Indian J. Pure Appl. Math. 32 (2001) 1565-1570). 相似文献
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18.
Hao Pan 《Discrete Mathematics》2006,306(17):2118-2127
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers. 相似文献
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