Asymptotische Entwicklung von verallgemeinerten Bernoullischen Funktionen und von Teilsummen Dirichletscher Reihen mit periodischer Koeffizientenfolge.
Asymptotische Untersuchungen über die Anzahl der Teiler von n.
Aufeinanderfolgende Elemente in multiplikativen Zahlenmengen.
Aus der Theorie der zahlentheoretischen Funktionen.
Autour du théorème de Bombieri-Vinogradov. II
Average multiplicative orders of elements modulo n
Average orders of multiplicative arithmetical functions of integer matrices
Average Value of the Euler Function on Binary Palindromes
We study values of the Euler function φ(n) taken on binary palindromes of even length. In particular, if denotes the set of binary palindromes with precisely 2ℓ binary digits, we derive an asymptotic formula for the average value of the Euler function on .
Averages of Euler products, distribution of singular series and the ubiquity of Poisson distribution
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Beatty sequences and multiplicative number theory
Bemerkung zu einem Ergebnis von Erdös über befreundete Zahlen.
Billiard complexity in the hypercube
We consider the billiard map in the hypercube of . We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that is the order of magnitude of the complexity.
Binomial expected values of arithmetical functions.
Carmichael's lambda function
Changes of sign of error terms related to Euler's function and to divisor functions.
Changes of sign of error terms related to Euler's function and to divisor functions II
Charakterisierung der additiven, fast-geraden Funktionen.
Chebotarev formations and quantitative aspects of non-unique factorizations
Circles passing through five or more integer points
We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let be the number of cyclic polygons...