19 citations · 48 across the 32 of their papers we have counts for
13 papers · 1 filter
Critical probabilistic characteristics of the Cramér model for primes and arithmetical properties
Michel Weber
This work is a probabilistic study of the 'primes' of the Cramér model. We prove that there exists a set of integers of density 1 such that \begin{equation}\liminf_{ \…
On good universality and the Riemann hypothesis
Jean-Louis Verger-Gaugry, Radhakrishnan Nair, Michel Weber
We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisation…
On the Uniform Distribution (mod 1) of the Farey Sequence, quadratic Farey and Riemann sums with a remark on local integrals of
Michel Weber
For -periodic functions satisfying only a weak local regularity assumption of Dini's type at rational points of , we study the Farey sums $$F_n(f)= \sum_{\frac{\k}ł\i…
An extension of a result of Erdös and Zaremba
Michel Jean Georges Weber
Erdös and Zaremba showed that $ \limsup_{n\to \infty} \frac{Φ(n)}{(\log\log n)^2}=e^\g$, $\g$ being Euler's constant, where . We extend this resul…
On the equation restricted to factor closed sets
Sanying Shi, Michel Weber
We study the number of solutions of the diophantine equation , where , , and is a factor clos…
Cauchy Means of Dirichlet polynomials
Michel Weber
We study Cauchy means of Dirichlet polynomials $$\int_\R \Big|\sum_{n=1}^N \frac{1}{ n^{\s+ ist}} \Big|^{2q} \frac{\dd t}{π( t^2+1)}.$$ These integrals were investigated when $q=1,…