Discrete uniform limit law for additive functions on shifted primes
نویسندگان
چکیده
منابع مشابه
Additive Functions on Shifted Primes
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes. A real-valued function / defined on the positive integers is additive if it satisfies f(rs) = f(r) + f(s) whenever r and s are coprime. Such functions are determined by their values on the prime-powers. For additive arithmetic function /, let Q denote the frequency...
متن کاملDivisors of Shifted Primes
Abstract. We bound from below the number of shifted primes p+s ≤ x that have a divisor in a given interval (y, z]. Kevin Ford has obtained upper bounds of the expected order of magnitude on this quantity as well as lower bounds in a special case of the parameters y and z. We supply here the corresponding lower bounds in a broad range of the parameters y and z. As expected, these bounds depend h...
متن کاملOn the strong law of large numbers and additive functions
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑N n=1 f(n)Xn ∑N n=1 f(n) = EX a.s.
متن کاملSome Uniform Limit Results in Additive Regression Model
For 0 < p < ∞, the optimal Lp rate of convergence of a nonparametric estimate of m is of order n −k 2k+d when m is assumed to be a k-times differentiable function and for p = ∞, the optimal rate is (n−1 log n) k 2k+d (see, Stone (1985)). This rate of convergence which depends on the dimension d of the covariable X becomes worse as the dimensionality of the problem increases. In the literature, ...
متن کاملcient Primes for Discrete Log
This paper presents a method for generating prime moduli with a special form which can simplify the modular reduction process and reduce the storage requirement. Such moduli will be particularly useful for implementing discrete log cryptosystems under the environment with limited computing and storage resources.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis: Modelling and Control
سال: 2016
ISSN: 2335-8963,1392-5113
DOI: 10.15388/na.2016.4.1