On Sums of Two Coprime k-th Powers.
On sums of two cubes: an Ω₊-estimate for the error term
The arithmetic function counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a sufficiently...
On sums of two kth powers: a mean-square asymptotics over short intervals
On sums of two kth powers: an asymptotic formula for the mean square of the error term
On the arithmetical functions and .
On the asymmetric divisor problem with congruence conditions
A certain generalized divisor function is studied which counts the number of factorizations of a natural number into integer powers with prescribed exponents under certain congruence restrictions. An -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
On the asymptotic behavior of the Dickman-de Bruijn function.
On the Asymptotic Behaviour of Sums ...g (n) ...x/n...
On the asymptotic formulae for some functions connected with powers of the zeta function
On the asymptotic formulas for powerful numbers.
On the Average Number of Direct Factors of a Finite Abelian Group.
On the average number of direct factors of a finite abelian group
On the average number of direct factors of a finite Abelian group
On the average number of direct factors of finite abelian groups
On the average number of direct factors of finite abelian groups (II)
On the average number of unitary factors of finite abelian groups
On the average of the sum-of-a-divisors function
We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
On the average of the sum-of-p-prime-divisors function
On the average orders of a class of divisor functions.
On the -ary expansion of an algebraic number