A problem in comparative prime number theory
A Tauberian theorem for the Ingham summation method
Arithmetical Tauberian theorems
Asymptotics of counts of small components in random structures and models of coagulation-fragmentation
We establish necessary and sufficient conditions for the convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. The multiplicative measures depict distributions of component spectra of random structures and also the equilibria of classic models of statistical mechanics and stochastic processes of coagulation-fragmentation. We show that the convergence of multiplicative measures is equivalent to the asymptotic independence of counts of...
Correction to my paper «Sull'analogo della formula di Selberg nei corpi di funzioni»
This Note completes and corrects a preceding Lincean Note by introducing through a tauberian theorem an appropriate condition which removes a counter-example provided by Dr. Zhang.
Ein Tauber-Satz mit Restglied für die Laplace-Transformation.
Eine Anwendungen Tauberscher Sätze in der Zahlentheorie. A.
Einige Anwendungen Tauberscher Sätze in der Zahlentheorie. B.
Einige Anwendungen Tauberscher Sätze in der Zahlentheorie. C.
Ingham Tauberian theorem with an estimate for the error term.
On some tauberian theorems related to the prime number theorem
On Summatory Functions of Additive Functions and Regular Variation
On the Tauberian constant in the Ikehara theorem
Oscillation of Mertens’ product formula
Mertens’ product formula asserts thatas . Calculation shows that the right side of the formula exceeds the left side for . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on , this and a complementary inequality might change their sense for sufficiently large values of . We show this to be the case.
Solution to a problem of Bombieri
We solve a problem of Bombieri, stated in connection with the «prime number theorem» for function fields.
Tauberian theorems for sum sets
The prime number theorem for Beurling's generalized numbers. New cases
The quickest proof of the prime number theorem
Two elementary proofs of Halász's theorem.
Volumes of symmetric spaces via lattice points.