Mod–discrete Expansions
نویسنده
چکیده
In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law cannot be expected. The setting is one in which the simplest approximation to the n’th random variable Xn is by a particular member Rn of a given family of distributions, whose variance increases with n. The basic assumption is that the ratio of the characteristic function of Xn and that of Rn converges to a limit in a prescribed fashion. Our results cover a number of classical examples in probability theory, combinatorics and number theory.
منابع مشابه
On the real quadratic fields with certain continued fraction expansions and fundamental units
The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element where $dequiv 2,3( mod 4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and $n_d$ and $m_d...
متن کاملMatrix expansions for computing the discrete hartley transform for blocklength N ≡ 0 (mod 4)
Abstract— A new fast algorithm for computing the discrete Hartley transform (DHT) is presented, which is based on the expansion of the transform matrix. The algorithm presents a better performance, in terms of multiplicative complexity, than previously known fast Hartley transform algorithms and same performance, in terms of additive complexity, than Split-Radix algorithm. A detailed descriptio...
متن کاملDigital expansions with negative real bases
Similarly to Parry’s characterization of β-expansions of real numbers in real bases β > 1, Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of 1 in base β > 1. In the same vein, we characterize the sequences that occur as (−β)-expansion of −β β+1 for some β > 1. These...
متن کاملA New Algorithm for Inversion mod p
A new algorithm for computing x = a−1 (mod pk) is introduced. It is based on the exact solution of linear equations using p-adic expansions. It starts with the initial value c = a−1 (mod p) and iteratively computes the digits of the inverse x = a−1 (mod pk) in base p. The mod 2 version of the algorithm is significantly more efficient than the existing algorithms for small values of k. We also d...
متن کاملDiscrete Ramanujan-Fourier Transform of Even Functions (mod $r$)
An arithmetical function f is said to be even (mod r) if f (n) = f ((n, r)) for all n ∈ Z + , where (n, r) is the greatest common divisor of n and r. We adopt a linear algebraic approach to show that the Discrete Fourier Transform of an even function (mod r) can be written in terms of Ramanujan's sum and may thus be referred to as the Discrete Ramanujan-Fourier Transform.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009