On short sums of certain multiplicative functions.
On sums and differences of two coprime kth powers
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 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 average order of the lattice rest of a convex body
On the circle problem with general weight
On the circle problem with polynomial weight
On the class number of binary quadratic forms: An omega estimate for the error term.
On the distribution of integral and prime divisors with equal norms
In finite Galois extensions of with pairwise coprime discriminants the integral and the prime divisors subject to the condition are equidistributed in the sense of E. Hecke.
On the distribution of kth powers of integral quaternions
On the distribution of squares of integral Cayley numbers
On the distribution of squares of integral quaternions
On the distribution of squares of integral quaternions II
On the distribution of the free path length of the linear flow in a honeycomb
Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this result leads...
On the index of the boundary points of four-dimensional lattices that are admissible for a cube.
On the k-free divisor problem
On the lattice point problem for ellipsoids