Add to ORKGAbstract. Let!.n / denote the number of prime divisors of n and let˜.n / denote the number of prime power di-visors of n. We obtain upper bounds for the lengths of the longest intervals below x where!.n/, respectively˜.n/, remains constant. Similarly we consider the corresponding problems where the numbers!.n/, respectively˜.n/, are required to be all different on an interval. We show that the number of solutions g.n / to the equation mC!.m / D n is an unbounded function of n, thus answering a question posed in an earlier paper in this series. A principal tool is a Turán-Kubilius type inequality for additive functions on arithmetic progressions with a large modulus. Key words: Turán-Kubilius inequality, additive functions, prime divisor
AbstractIn this paper we study additive functions on arithmetic progressions with large moduli. We a...
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modu...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
Since Kubilius in 1983 proved that the Turan-Kubilius inequality holds with the constant close to 1....
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
This thesis gives some order estimates and asymptotic formulae associated with general classes of no...
This dissertation focuses on three problems in analytic number theory, one of a multiplicative natur...
In this paper we consider an analogue of the problem of Erdos and Woods for arithmetic progressions....
International audienceIn 1934 Turan proved that if f(n) is an additive arithmetic function satisfyin...
We shall prove here the following bounds for the | frequency of large differences, dn = Pn + i~Pn>...
This paper is concerned with formulation and demonstration of new versions of equations that can hel...
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that...
In this thesis we prove several different results about the number of primes represented by linear f...
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. ...
AbstractIn this paper we study additive functions on arithmetic progressions with large moduli. We a...
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modu...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
AbstractLet ν(n) denote the number of distinct prime factors of n. We show that the equation n + ν(n...
Since Kubilius in 1983 proved that the Turan-Kubilius inequality holds with the constant close to 1....
Abstract. For each of the functions f ∈ {ϕ, σ, ω, τ} and every natural number K, we show that there ...
This thesis gives some order estimates and asymptotic formulae associated with general classes of no...
This dissertation focuses on three problems in analytic number theory, one of a multiplicative natur...
In this paper we consider an analogue of the problem of Erdos and Woods for arithmetic progressions....
International audienceIn 1934 Turan proved that if f(n) is an additive arithmetic function satisfyin...
We shall prove here the following bounds for the | frequency of large differences, dn = Pn + i~Pn>...
This paper is concerned with formulation and demonstration of new versions of equations that can hel...
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that...
In this thesis we prove several different results about the number of primes represented by linear f...
This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. ...
AbstractIn this paper we study additive functions on arithmetic progressions with large moduli. We a...
We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modu...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...