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1.
Hao Pan 《Discrete Mathematics》2006,306(16):1921-1940
By a very simple argument, we prove that if l,m,n∈{0,1,2,…} then
2.
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
3.
Zhi-Wei Sun 《Journal of Number Theory》2011,131(11):2219-2238
It is known that
5.
Hui-Qin Cao 《Journal of Number Theory》2009,129(8):1813-1819
In the paper, we generalize some congruences of Lehmer and prove that for any positive integer n with (n,6)=1
6.
Guodong Liu 《Journal of Number Theory》2008,128(12):3063-3071
In this paper, we establish some identities involving the Euler numbers, the Euler numbers of order 2 and the central factorial numbers, and give a new proof of a classical result due to M.A. Stern.
Video abstract
For a video summary of this paper, please visit http://www.youtube.com/watch?v=kdNsdTDA-FE. 相似文献7.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
8.
Text
In this paper we apply Yamamoto's Theorem [Y. Yamamoto, Dirichlet series with periodic coefficients, in: Proc. Intern. Sympos. “Algebraic Number Theory”, Kyoto, 1976, JSPS, Tokyo, 1977, pp. 275-289] to find the residue modulo a prime power of the linear combination of Dirichlet L-function values L(s,χ) at positive integral arguments s such that s and χ are of the same parity, in terms of Euler numbers, whereby we obtain the finite expressions for short interval character sums. The results obtained generalize the previous results pertaining to the congruences modulo a prime power of the class numbers as the special case of s=1.Video
For a video summary of this paper, please visit http://www.youtube.com/watch?v=_KAv4FCdVUs. 相似文献9.
Hao Pan 《Journal of Number Theory》2008,128(6):1646-1654
Let e?1 and b?2 be integers. For a positive integer with 0?aj<b, define
10.
Zhi-Wei Sun 《Journal of Number Theory》2005,115(2):371-380
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M.A. Stern. 相似文献
11.
Zhi-Wei Sun 《Journal of Number Theory》2011,131(12):2387-2397
The nth Delannoy number and the nth Schröder number given by
12.
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
13.
Sandro Mattarei 《Journal of Number Theory》2008,128(1):49-58
We investigate when the sequence of binomial coefficients modulo a prime p, for a fixed positive integer k, satisfies a linear recurrence relation of (positive) degree h in the finite range 0?i?k. In particular, we prove that this cannot occur if 2h?k<p−h. This hypothesis can be weakened to 2h?k<p if we assume, in addition, that the characteristic polynomial of the relation does not have −1 as a root. We apply our results to recover a known bound for the number of points of a Fermat curve over a finite field. 相似文献
14.
By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers n1,…,nm, nm+1=n1, and any nonnegative integer r, the expression
15.
Hao Pan 《Journal of Combinatorial Theory, Series A》2006,113(1):156-175
Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki's and Matiyasevich's identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun. 相似文献
16.
Sandro Mattarei 《Journal of Number Theory》2006,117(2):471-481
We prove that if the signed binomial coefficient viewed modulo p is a periodic function of i with period h in the range 0?i?k, then k+1 is a power of p, provided h is not too large compared to k. (In particular, 2h?k suffices). As an application, we prove that if G and H are multiplicative subgroups of a finite field, with H<G, and such that 1-α∈G for all α∈G?H, then G∪{0} is a subfield. 相似文献
17.
Li-Lu Zhao 《Journal of Number Theory》2010,130(4):930-935
Let n be a positive odd integer and let p>n+1 be a prime. We mainly derive the following congruence:
18.
Let q?2 be an integer, χ be any non-principal character mod q, and H=H(q)?q. In this paper the authors prove some estimates for character sums of the form
19.
Toufik Mansour 《Discrete Applied Mathematics》2007,155(11):1430-1440
Baxter studied a particular class of permutations by considering fixed points of the composite of commuting functions. This class is called Baxter permutations. In this paper we investigate the number of 123-avoiding Baxter permutations of length n that also avoid (or contain a prescribed number of occurrences of) another certain pattern of length k. In several interesting cases the generating function depends only on k and is expressed via the generating function for the Padovan numbers. 相似文献
20.
It was discovered some years ago that there exist non-integer real numbers q>1 for which only one sequence (ci) of integers ci∈[0,q) satisfies the equality . The set of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation.In this paper we consider for each fixed q>1 the set Uq of real numbers x having a unique representation of the form with integers ci belonging to [0,q). We carry out a detailed topological study of these sets. For instance, we characterize their closures, and we determine those bases q for which Uq is closed or even a Cantor set. We also study the set consisting of all sequences (ci) of integers ci∈[0,q) such that . We determine the numbers r>1 for which the map (defined on (1,∞)) is constant in a neighborhood of r and the numbers q>1 for which is a subshift or a subshift of finite type. 相似文献