17 citations · 84 across the 18 of their papers we have counts for
20 papers
A lower bound for the number of Egyptian fractions
Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1
An Egyptian fraction is a sum of the form where are distinct positive integers. We prove explicit lower bounds for the cardinality of the…
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{…
Breaking the 4 barrier for the bound of a generating set of the class group
Loïc Grenié, Giuseppe Molteni
Let be a field of degree and discriminant with absolute value . Under the assumption of the validity of the Generalized Riemann Hypothesis, we provide a new algorithm to…
Deterministic Bridge Regression for Compressive Classification
Kar-Ann Toh, Giuseppe Molteni, Zhiping Lin
Pattern classification with compact representation is an important component in machine intelligence. In this work, an analytic bridge solution is proposed for compressive classifi…
An elementary proof for a generalization of a Pohst's inequality
Francesco Battistoni, Giuseppe Molteni
Let and where the supremum is taken over the $n…
Counting Egyptian fractions
Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1
For any integer , let be the set of all Egyptian fractions employing denominators less than or equal to . We give upper and lower bounds for the cardi…
Conditional upper bound for the k-th prime ideal with given Artin symbol
Loïc Grenié, Giuseppe Molteni
We prove an explicit upper bound for the k-th prime ideal with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.
Small values of signed harmonic sums
Sandro Bettin, Giuseppe Molteni, Carlo Sanna
For every and every integer , let be the minimum of the distance of from the sums , where $s_1, \ldots, s_n \in \{-1…
Greedy approximations by signed harmonic sums and the Thue--Morse sequence
Sandro Bettin, Giuseppe Molteni, Carlo Sanna
Given a real number , we study the approximation of by signed harmonic sums , where the sequence of signs i…
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…
A conjectural extension of Hecke's converse theorem
Sandro Bettin, Jonathan W. Bober, Andrew R. Booker +6
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main…
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 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.
An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman
Loïc Grenié, Giuseppe Molteni
In [BDyDF08] Belabas, Diaz y Diaz and Friedman show a way to determine, assuming the Generalized Riemann Hypothesis, a set of prime ideals that generate the class group of a number…
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…