We study the mean value of generalized divisor functions $τ_κ(n)$ over integers without large prime factors (here $κ>0$). We relate this problem to the computation of the ratio $Ψ(x^{1/κ}, y)^κ/Ψ(x, y)$ , involving the y-smooth numbers counting function. We establish an inverse theorem, giving limitations on the range in $(x,y)$ in which this ratio can be asymptotically estimated uniformly in $κ$
summary:A certain generalized divisor function $d^*(n)$ is studied which counts the number of factor...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
We study the mean value of generalized divisor functions $τ_κ(n)$ over integers without large prime ...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
International audienceA number is said to be y-friable if it has no prime factor greater than y. In ...
AbstractLet {ϵd} be a sequence of nonnegative numbers and f(n) = Σ ϵd, the sum being over divisors d...
Let α(n) denote the Fourier coefficients of cusp forms or the number of divisors of n. Estimates of ...
AbstractLet d(ω; α, γ) be the number of divisors of the Gaussian integer ω which lie in the arithmet...
Call integer $y$ friable if its largest prime factor does not exceed $y$. We study friable integers ...
AbstractLet ζ be the Riemann zeta-function and write ζ(s)2 = Σn >- 1 dz(n)n−s for real s > 1, z > 1,...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
Abstract. We use the saddle-point method (due to Hildebrand–Tenen-baum [3]) to study the asymptotic ...
We investigate the first and second moments of shifted convolutions of the generalized divisor funct...
summary:A certain generalized divisor function $d^*(n)$ is studied which counts the number of factor...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
We study the mean value of generalized divisor functions $τ_κ(n)$ over integers without large prime ...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
International audienceA number is said to be y-friable if it has no prime factor greater than y. In ...
AbstractLet {ϵd} be a sequence of nonnegative numbers and f(n) = Σ ϵd, the sum being over divisors d...
Let α(n) denote the Fourier coefficients of cusp forms or the number of divisors of n. Estimates of ...
AbstractLet d(ω; α, γ) be the number of divisors of the Gaussian integer ω which lie in the arithmet...
Call integer $y$ friable if its largest prime factor does not exceed $y$. We study friable integers ...
AbstractLet ζ be the Riemann zeta-function and write ζ(s)2 = Σn >- 1 dz(n)n−s for real s > 1, z > 1,...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
Abstract. We use the saddle-point method (due to Hildebrand–Tenen-baum [3]) to study the asymptotic ...
We investigate the first and second moments of shifted convolutions of the generalized divisor funct...
summary:A certain generalized divisor function $d^*(n)$ is studied which counts the number of factor...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
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