Théorèmes de densité dans
Théorèmes d'oscillations et fonction de Möbius.
Theorie der Gitterpunkte.
Third power moments of the error terms corresponding to certain arithmetic functions.
Three two-dimensional Weyl steps in the circle problem I. The Hessian determinant
1. Summary. In a sequence of three papers we study the circle problem and its generalization involving the logarithmic mean. Most of the deeper results in this area depend on estimates of exponential sums. For the circle problem itself Chen has carried out such estimates using three two-dimensional Weyl steps with complicated techniques. We make the same Weyl steps but our approach is simpler and clearer. Crucial is a good understanding of the Hessian determinant that appears and a simple...
Three two-dimensional Weyl steps in the circle problem II. The logarithmic Riesz mean for a class of arithmetic functions
1. Summary. In Part II we study arithmetic functions whose Dirichlet series satisfy a rather general type of functional equation. For the logarithmic Riesz mean of these functions we give a representation involving finite trigonometric sums. An essential tool here is the saddle point method. Estimation of the exponential sums in the special case of the circle problem will be the topic of Part III.
Topological aspects of infinitude of primes in arithmetic progressions
We investigate properties of coset topologies on commutative domains with an identity, in particular, the 𝓢-coprime topologies defined by Marko and Porubský (2012) and akin to the topology defined by Furstenberg (1955) in his proof of the infinitude of rational primes. We extend results about the infinitude of prime or maximal ideals related to the Dirichlet theorem on the infinitude of primes from Knopfmacher and Porubský (1997), and correct some results from that paper. Then we determine cluster...
Totally multiplicative sequences with values ... 1 which exclude four consecutive values of 1.
Triangular numbers whose sum of divisors is also triangular
Trigonometrische Reihen über multiplikativen Zahlenmengen.
Trivial Selmer groups and even partitions of a graph.
Two arithmetic functions and asymptotic densities of related sets
Two elementary proofs of Halász's theorem.
Two remarks in prime number theory
Übe die Anzahl Abelscher Gruppen gegebener Ordnung. II.
Über additive zahlentheoretische Funktionen.
Über allgemeine Sequenzen der Länge 3 von Legendresymbolen.
Über binäre additive Probleme.
Über das Primzahl-Zwillingsproblem.
Über das summatorische Verhalten zahlentheoretischer Funktionen.