A mean value theorem on differences of two k-th powers of numbers in residue classes.
On the distribution of squares of integral quaternions
On the distribution of squares of integral quaternions II
Counting linearly ordered spaces
For a transfinite cardinal κ and i ∈ 0,1,2 let be the class of all linearly ordered spaces X of size κ such that X is totally disconnected when i = 0, the topology of X is generated by a dense linear ordering of X when i = 1, and X is compact when i = 2. Thus every space in ℒ₁(κ) ∩ ℒ₂(κ) is connected and hence ℒ₁(κ) ∩ ℒ₂(κ) = ∅ if , and ℒ₀(κ) ∩ ℒ₁(κ) ∩ ℒ₂(κ) = ∅ for arbitrary κ. All spaces in ℒ₁(ℵ₀) are homeomorphic, while ℒ₂(ℵ₀) contains precisely ℵ₁ spaces up to homeomorphism. The class ℒ₁(κ)...
On the differentiability of certain saltus functions
We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
On the circle problem with general weight
The two parameter ellipse problem
On the number of lattice points in certain planar segments
On the circle problem with polynomial weight
On certain separable and connected refinements of the Euclidean topology
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