Stability aspects of arithmetic functions, II

Diophantine Approximation with Arithmetic Functions, Ii

We prove that real numbers can be well-approximated by the normalized Fourier coefficients of newforms.

On the Composition of Some Arithmetic Functions, Ii

We study certain properties and conjuctures on the composition of the arithmetic functions σ, φ, ψ, where σ is the sum of divisors function, φ is Euler’s totient, and ψ is Dedekind’s function.

On Locally Repeated Values of Certain Arithmetic Functions . Ii

which is nearly 1 if K is large . Thus if n and n+1 both satisfy (1 .3) and if we view v(n) and v(n+l) as "independent events", then the "probability" that (L2) holds should be at least (2K Vlog log n)-1 . Summing these probabilities would then give order of magnitude x1f log log x solutions n of (1 .2) with n-x, thus supporting the conjecture. A refinement of this heuristic argument even sugge...

Arithmetic Aspects of Atomic Structures

Geometric and design-theoretic aspects of semibent functions II

This paper is the successor of [8]. We now consider semibent functions with a linear structure. Semibent functions of partial spread type with a linear structure seem to be rare. We distinguish four classes of such semibent functions. For three classes we exhibit some examples.