On the coefficients cn in the expansion ... .
On the congruence
On the counting function for sums of two squares
On the critical pair theory in ℤ/pℤ
On the Davenport constant and group algebras
For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence over G such that for all . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for which (G) -...
On the differences of the partition function
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 estimation of Schnirelman's constant.
On the exceptional set for the -twin primes problem
On the exceptional set of Goldbach numbers in a short interval
On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables
We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.
On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer.
On the Fourier coefficients of small positive powers of 0 ... .
On the Goldbach conjecture and the consistency of general recursive arithemetic.
On the index of the boundary points of four-dimensional lattices that are admissible for a cube.