10 citations · 58 across the 28 of their papers we have counts for
4 papers · 1 filter
Chebyshev's bias and generalized Riemann hypothesis
Adel Alamadhi, Michel Planat, Patrick Solé
It is well known that (i) up to the (very large) Skewes' number \cite{Bays00}. But, according to a Littlewood's theorem, there exist in…
Efficient prime counting and the Chebyshev primes
Michel Planat, Patrick Solé
The function $ε(x)=\mbox{li}(x)-π(x)$ is known to be positive up to the (very large) Skewes' number. Besides, according to Robin's work, the functions $ε_θ(x)=\mbox{li}[θ(x)]-π(x)$…
Pauli graphs, Riemann hypothesis, Goldbach pairs
Michel Planat, Fabio Anselmi, Patrick Solé
Let consider the Pauli group with unitary quantum generators (shift) and (clock) acting on the vectors of the -dimensional Hilbert space via $X|s>…
Lattice Codes for the Wiretap Gaussian Channel: Construction and Analysis
Frédérique Oggier, Patrick Solé, Jean-Claude Belfiore
We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, a…