49 citations · 178 across the 28 of their papers we have counts for
4 papers · 2 filters
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…
Modularity and value distribution of quantum invariants of hyperbolic knots
Sandro Bettin, Sary Drappeau
We obtain an exact modularity relation for the -Pochhammer symbol. Using this formula, we show that Zagier's modularity conjecture for a knot essentially reduces to the arit…
Partial sums of the cotangent function
Sandro Bettin, Sary Drappeau
Nous prouvons l'existence de formules de réciprocité pour des sommes de la forme , où est une fonction par morceaux, qui…
Limit laws for rational continued fractions and value distribution of quantum modular forms
Sandro Bettin, Sary Drappeau
We study the limiting distributions of Birkhoff sums of a large class of cost functions (observables) evaluated along orbits, under the Gauss map, of rational numbers in or…