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...
Coincidences in the values of the Euler and Carmichael functions
Combinatoire du billard dans un polyèdre
Ces notes ont pour but de rassembler les différents résultats de combinatoire des mots relatifs au billard polygonal et polyédral. On commence par rappeler quelques notions de combinatoire, puis on définit le billard, les notions utiles en dynamique et le codage de l’application. On énonce alors les résultats connus en dimension deux puis trois.
Comparing the number of abelian groups and of semisimple rings of a given order
Completely q-multiplicative functions: the Mellin transform approach
Composite positive integers with an average prime factor
Computations concerning the conjecture of Mertens.
Concentration function of additive functions on shifted twin primes
Concentration function of additive functions on shifted twin primes
0. Introduction. The content of this paper is part of the author's Ph.D. thesis. The two new theorems in this paper provide upper bounds on the concentration function of additive functions evaluated on shifted γ-twin prime, where γ is any positive even integers. Both results are generalizations of theorems due to I. Z. Ruzsa, N. M. Timofeev, and P. D. T. A. Elliott.
Consecutive square-free values of the type ,
We show that for any given integer there exist infinitely many consecutive square-free numbers of the type , . We also establish an asymptotic formula for such that , are square-free. The method we used in this paper is due to Tolev.
Consequences of a theorem of Erdős-Prachar.
Construction of normal numbers via pseudo-polynomial prime sequences
We construct normal numbers in base q by concatenating q-ary expansions of pseudo-polynomials evaluated at primes. This extends a recent result by Tichy and the author.
Contributions to the Erdös-Szemerédi theory of sieved integers
Convolutions and Mean Square Estimates of Certain Number-theoretic Error Terms
Correction to the paper "On a kind of uniform distribution of values of multiplicative functions in residue classes", Acta Arithmetica 31(1976), pp. 291-294