202 citations
- Istituto Nazionale di Fisica Nucleare, Sezione di MilanoIT137 papers
- University of Milano-BicoccaIT99 papers
- University of MilanIT86 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano BicoccaIT67 papers
- Centre National de la Recherche ScientifiqueFR63 papers
- Imperial College LondonGB62 papers
- University of GenoaIT61 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di FirenzeIT60 papers
- Istituto Nazionale di Fisica Nucleare, Sezione di PisaIT60 papers
- Massachusetts Institute of TechnologyUS59 papers
- University of CagliariIT59 papers
- University of PisaIT59 papers
11 papers · 1 filter
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…
Mixed norms of the lattice point discrepancy
Leonardo Colzani, Bianca Gariboldi, Giacomo Gigante
We estimate some mixed norms of the discrepancy between the volume and the number of integer points in , a dilated by a factor and translated…
Explicit Short Intervals for Primes in Arithmetic Progressions on GRH
Adrian W. Dudek, Loïc Grenié, Giuseppe Molteni
We prove explicit versions of Cramér's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
Primes and prime ideals in short intervals
L. Grenié, G. Molteni, A. Perelli
We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in t…
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.