共查询到20条相似文献,搜索用时 406 毫秒
1.
Byungchan Kim 《Journal of Number Theory》2012,132(6):1306-1313
We study the number of partitions of n into k different parts by constructing a generating function. As an application, we will prove mysterious identities involving convolution of divisor functions and a sum over partitions. By using a congruence property of the overpartition function, we investigate values of a certain convolution sum of two divisor functions modulo 8. 相似文献
2.
In this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the maximum and minimum values of the divisor function on intervals of length k. 相似文献
3.
4.
J. Jorgenson 《Israel Journal of Mathematics》1992,77(3):273-284
In this note we will identify the divisor of any fixed directional derivative of the Riemann theta function evaluated along
the theta divisor with the divisor formed from ag−1 dimensional subspace of holomorphic one-forms from the underlying Riemann surface. 相似文献
5.
关于F.Smarandache LCM函数与除数函数的一个混合均值 总被引:4,自引:2,他引:2
吕国亮 《纯粹数学与应用数学》2007,23(3):315-318
利用初等及解析方法研究函数SL(n)与Dirichlet除数函数的加权均值问题,并获得一个有趣的渐近公式. 相似文献
6.
李毅君 《数学的实践与认识》2012,42(19)
对任意正整数n,设d(n)表示n的Dirichlet除数函数,即就是n的所有不同正因数的个数.Smarandache可求积因数对问题是:求所有正整数对m及n使得d(m)+d(n)=d(mn).主要目的是利用初等方法以及除数函数的性质研究这一问题,并给予彻底解决.具体地说也就是证明了正整数对m及n满足方程d(m)+d(n)=d(mn)当且仅当(m,n)=(pq~α,q)或者(m,n)=(p,p~αq),其中p及q为不同的素数,α为非负整数. 相似文献
7.
E. Krätzel 《Acta Mathematica Hungarica》2010,126(3):258-278
In this article we consider three problems: 1. The asymptotic behaviour of the quadratic moment of the exponential divisor
function. 2. The distribution of powerful integers of type 4. 3. The average number of direct factors of a finite Abelian
group. We prove new estimates for the error terms in the asymptotic representations. For this purpose new estimates in the
general four-dimensional divisor problem are needed. 相似文献
8.
We derive an explicit formula for the moments of the probability density function of a class of functions. An application of this shows that the density function of the error term in the Pilz divisor problem is asymmetric.
9.
The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use... 相似文献
10.
When the seats in a parliamentary body are to be allocated proportionally to some given weights, such as vote counts or population data, divisor methods form a prime class to carry out the apportionment. We present a new characterization of divisor methods, via primal and dual optimization problems. The primal goal function is a cumulative product of the discontinuity points of the rounding rule. The variables of the dual problem are the multipliers used to scale the weights before they get rounded. Our approach embraces pervious and impervious divisor methods, and vector and matrix problems. 相似文献
11.
A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of constants, then it also can be represented as an imaginary quadratic extension of the rational function field. The arithmetic in the divisor class group can be realized in the second case by Cantor's algorithm. We show that in the first case one can compute in the divisor class group of the function field using reduced ideals and distances of ideals in the orders involved. Furthermore, we show how the two representations are connected and compare the computational complexity.
12.
Let S = {x1, x2,..., xn} be a set of distinct positive integers. The n x n matrix (S) whose i, j-entry is the greatest common divisor (xi, xj) of xi and xj is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d) = 1. The greatest common unitary divisor (GCUD) matrix (S**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S**) ≥ det(S), where the equality holds if and Only if (S**) = (S). 相似文献
13.
《Expositiones Mathematicae》2022,40(3):665-678
In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function fully explicit. 相似文献
14.
We consider a sequence of distributions defined via the generalized divisor function. We describe the possible limit distributions and estimate the remainder terms. 相似文献
15.
Ritabrata Munshi 《The Ramanujan Journal》2011,25(2):195-201
We give certain optimal inequalities for the divisor function. Such inequalities are useful in estimating the sums of divisor
functions which are required in many standard arguments in analytic number theory. 相似文献
16.
Daniel Peralta-Salas Álvaro del Pino Francisco Presas 《Israel Journal of Mathematics》2016,212(1):443-472
We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by É. Fouvry, S. Ganguly, E. Kowalski and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered. 相似文献
17.
本文研究了多维除数函数d_k(n)在特殊序列[n~c]上的分布。利用指数和方法中一些新成果,证明了:当实数c满足1相似文献
18.
Toru Tsukioka 《Mathematische Zeitschrift》2012,271(1-2):555-564
The minimum of intersection numbers of the anti-canonical divisor with rational curves on a Fano manifold is called pseudo-index. It is expected that the intersection number of anti-canonical divisor attains to the minimum on an extremal ray, i.e. there exists an extremal rational curve whose intersection number with the anti-canonical divisor equals the pseudo-index. In this note, we prove this for smooth Fano four-folds having birational contractions. 相似文献
19.
The greatest common divisor of two integers cannot be
generated in a uniformly bounded number of steps from those integers
using arithmetic operations. The proof uses an elementary model-theoretic
construction that enables us to focus on
integers with transcendental ratio.
This unboundedness result is part of the solution of a problem posed
by Y. Moschovakis on limitations of primitive recursive
algorithms for computing the greatest common divisor function. 相似文献
20.
图T1,1,m与Q(3,n)中有路因子的充分必要条件及T1,1,m的匹配等价类 总被引:1,自引:0,他引:1
如果一个图的匹配多项式可以被一个路的匹配多项式整除,我们就称此路是该图的一个路因子,路因子在刻画图的匹配等价类,研究匹配唯一性方面有很重要的作用.本文得到了图T1,1.m与图Q(3,n)中有路因子的充分必要条件. 相似文献