Multiplikative Funktionen auf schnell wachsenden Folgen.
Multiplikative Funktionen mehrerer Variablen.
Natural divisors and the brownian motion
A model of the Brownian motion defined in terms of the natural divisors is proposed and weak convergence of the related measures in the space [0,1] is proved. An analogon of the Erdös arcsine law, known for the prime divisors [6] (see [14] for the proof), is obtained. These results together with the author’s investigation [15] extend the systematic study [9] of the distribution of natural divisors. Our approach is based upon the functional limit theorems of probability theory.
Nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines
We show that the density functions of nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines are described by the M-function which appears in value distribution of the logarithmic derivative of the Riemann zeta-function on vertical lines.
Neuere Untersuchungen über die Jacobsthal-Funktion g(n).
New Omega Theorems for Two Classical Lattice Points Problems.
New prime-producing quadratic polynomials associated with class number one or two.
Nilpotents in semigroups of partial one-to-one order-preserving mappings.
Nombres ayant de grands facteurs premiers
Nombres hautement composés
Nombres 𝓑-libres dans les petits intervalles
Nombres premiers dans la suite [un2].
Nombres premiers et vibrations
Nombres premiers généralisés et équirépartition modulo 1
Nombres presque premiers et sommes trigonométriques
Nombres presque-premiers dans de petits intervalles
(Non)Automaticity of number theoretic functions
Denote by Liouville’s function concerning the parity of the number of prime divisors of . Using a theorem of Allouche, Mendès France, and Peyrière and many classical results from the theory of the distribution of prime numbers, we prove that is not –automatic for any . This yields that is transcendental over for any prime . Similar results are proven (or reproven) for many common number–theoretic functions, including , , , , , and others.
Non-divisibility of some multiplicative functions
Non-unique factorizations in orders of global fields.
Normal numbers and the middle prime factor of an integer
Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.