19 citations · 48 across the 32 of their papers we have counts for
42 papers
On Rozanov's Theorem and strenghtened asymptotic uniform distribution
Michel J. G. Weber
For sums , of independent random variables taking values in we prove, as a consequence of a more general result, that if (i) For some fu…
A uniform semi-local limit theorem along sets of multiples for sums of i.i.d. random variables
Michel J. G. Weber
Let be a square integrable random variable with basic probability space $(Ø, \A, ¶)$, taking values in a lattice and such th…
On Mukhin's necessary and sufficient condition for the validity of the local limit theorem
Michel J. G. Weber
Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only pr…
Classical and Almost Sure Local Limit Theorems
Zbigniew Szewczak, Michel Weber
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, i…
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…