10 papers
Signed harmonic sums of integers with distinct prime factors
Alessandro Gambini, Remis Tonon, Alessandro Zaccagnini
We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.
An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications
Mattia Cafferata, Alberto Perelli, Alessandro Zaccagnini
We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.
A note on an average additive problem with prime numbers
Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interva…
Short intervals asymptotic formulae for binary problems with prime powers, II
Alessandro Languasco, Alessandro Zaccagnini
We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms and $n…
Short intervals asymptotic formulae for binary problems with prime powers
Alessandro Languasco, Alessandro Zaccagnini
We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms , with $\ell_1…
A Cesàro average for an additive problem with prime powers
Alessandro Languasco, Alessandro Zaccagnini
In this paper we extend and improve our results on weighted averages for the number of representations of an integer as a sum of two powers of primes. Let …