17 citations · 66 across the 9 of their papers we have counts for
9 papers
The first and second moment for the length of the period of the continued fraction expansion for
Francesco Battistoni, Loïc Grenié, Giuseppe Molteni
Let be any positive and non square integer. We prove an upper bound for the first two moments of the length of the period of the continued fraction expansion for $\sqrt{…
An effective Chebotarev density theorem under GRH
L. Grenié, G. Molteni
We prove an effective version of the Chebotarev theorem for the density of prime ideals with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for…
Explicit bounds for generators of the class group
Loïc Grenié, Giuseppe Molteni
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group of a number field may be generated using prime ideals whose…
Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II
Loïc Grenié, Giuseppe Molteni
We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
Primes in explicit short intervals on RH
Adrian Dudek, Loïc Grenié, Giuseppe Molteni
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
Zeros of Dedekind zeta functions under GRH
Loïc Grenié, Giuseppe Molteni
Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in . We also prove a bound for the multiplicity…
Explicit smoothed prime ideals theorems under GRH
Loïc Grenié, Giuseppe Molteni
Let be the Chebyshev function of a number field . Let and $ψ^{(2)}_{\mathbb K}(x):=2\int_{0}^…
Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH
Loïc Grenié, Giuseppe Molteni
Let $ψ_\K$ be the Chebyshev function of a number field $\K$. Under GRH we prove an explicit upper bound for $|ψ_\K(x)-x|$ in terms of the degree and the discriminant of $\K$. The n…
Comparison of semi-simplifications of Galois representations
Loic Grenie
Let G be the absolute Galois group of a global field. Let r1 and r2 be two p-adic, finite dimensional representations of G. Then there exists a finite number of primes q such that…