共查询到20条相似文献,搜索用时 10 毫秒
1.
Matti Jutila 《The Ramanujan Journal》2007,14(2):321-327
A simplified proof for a well-distribution property for rational numbers is given and a connection with Riemann’s Hypothesis
is pointed out. More precisely, we consider rational numbers with denominators of a given order of magnitude and show that
the number of such numbers lying in a short interval of given length is normally close to its expectation in a mean square
sense. The proof is elementary, using only Fourier series and Ramanujan sums. At the end of the paper, a variant of the circle
method is discussed as an application.
相似文献
2.
Saugata Basu Richard Pollack Marie-Franç oise Roy 《Proceedings of the American Mathematical Society》2005,133(4):965-974
Let be a real closed field and let and be finite subsets of such that the set has elements, the algebraic set defined by has dimension and the elements of and have degree at most . For each we denote the sum of the -th Betti numbers over the realizations of all sign conditions of on by . We prove that
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
This generalizes to all the higher Betti numbers the bound on . We also prove, using similar methods, that the sum of the Betti numbers of the intersection of with a closed semi-algebraic set, defined by a quantifier-free Boolean formula without negations with atoms of the form or for , is bounded by
making the bound more precise.
3.
Fred Richman 《Mathematical Logic Quarterly》2008,54(1):98-108
A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete Archimedean Heyting field, a terminal object in the category of Archimedean Heyting fields. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the
rational numbers is its only model among the groups that are embeddable in the group of all computable permutations.
Supported by a Scheme 2 grant from the London Mathematical Society.
__________
Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007. 相似文献
5.
6.
7.
8.
An algorithm for computing best complex ordinary rational functions is presented. The final step of the procedure consists of solving the system of nonlinear equations defined by the local Kolmogorov criterion before checking recently developed sufficient optimality and uniqueness conditions. Various numerical results are reported exhibiting, in particular, nonunique solutions, saddle points and locally best approximants that are not global. 相似文献
9.
10.
On Miki's identity for Bernoulli numbers 总被引:1,自引:0,他引:1
Ira M. Gessel 《Journal of Number Theory》2005,110(1):75-82
We give a short proof of Miki's identity for Bernoulli numbers,
11.
12.
设n为自然数,σ(n)表示n的所有正因子和函数.令d是n的真因子,若n满足σ(n)=2n-d,则称n为亏因子为d的亏完全数.本文给出了具有四个素因子的奇亏完全数的一些性质的刻画. 相似文献
13.
将二项式系数的性质应用到Lucas数列的研究中,并结合Fibonacci数列与Lucas数列的恒等式得到几个有趣的Lucas数列的同余式. 相似文献
14.
V. Stakėnas 《Lithuanian Mathematical Journal》2006,46(2):208-216
Let Q
+ denote the set of positive rational numbers. We define discrete probability measures ν
x
on the σ-algebra of subsets of Q
+.We introduce additive functions ƒ: Q
+ → G and obtain a bound for νx(ƒ (r) ∉ X+X−X) using a probability related to some independent random variables. This inequality is an analogue to that proved by I. Ruzsa
for additive arithmetical functions.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 256–266, April–June, 2006. 相似文献
15.
《Journal of Pure and Applied Algebra》2019,223(11):4677-4688
In this paper, we prove a conjecture by T. Suzuki, which says if a smooth Fano manifold satisfies some positivity condition on its Chern characters, then it can be covered by rational N-folds. We prove this conjecture by using purely combinatorial properties of Bernoulli numbers. 相似文献
16.
Mario DeFranco 《Journal of Difference Equations and Applications》2013,19(9):1101-1120
We present an analytic extension of the unsigned Stirling numbers of the first kind that is in a certain sense unique in its coincidence with the Stirling polynomials. We examine and compare our extension to previous extensions of (signed) Stirling numbers of the first kind given by Butzer et al. (2007, J. Difference Equ. Appl., 13) and of the unsigned numbers given by Adamchik (1997, J. Comput. Appl. Math., 79). We also see a connection to the Riemann zeta function. 相似文献
17.
We compute the distributions of the size of the jumps of an increasing Markov process on , and we give a necessary and sufficient condition in order to have only jumps of size one. 相似文献
18.
Francis C.S. Brown 《Discrete Mathematics》2007,307(14):1722-1736
Let σ=(σ1,…,σN), where σi=±1, and let C(σ) denote the number of permutations π of 1,2,…,N+1, whose up-down signature sign(π(i+1)-π(i))=σi, for i=1,…,N. We prove that the set of all up-down numbers C(σ) can be expressed by a single universal polynomial Φ, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that Φ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers C(σ), for fixed N. We prove a concise upper bound for C(σ), which describes the asymptotic behaviour of the up-down function C(σ) in the limit C(σ)?(N+1)!. 相似文献
19.
20.
《Indagationes Mathematicae》2017,28(1):84-90
In a recent paper, Byrnes et al. (2014) have developed some recurrence relations for the hypergeometric zeta functions. Moreover, the authors made two conjectures for arithmetical properties of the denominators of the reduced fraction of the hypergeometric Bernoulli numbers. In this paper, we prove these conjectures using some recurrence relations. Furthermore, we assert that the above properties hold for both Carlitz and Howard numbers. 相似文献