3 papers
math.NT2025
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…
math.NT2025
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 t…
math.NT2024
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{…