11 papers
Ranks of elliptic curves over of small degree in
Francesco Battistoni, Sandro Bettin, Christophe Delaunay
We study elliptic surfaces over with coefficients of a Weierstrass model being polynomials in with degree at most 2. We derive an explicit expressio…
Effective estimation of some oscillatory integrals related to infinitely divisible distributions
Sandro Bettin, Sary Drappeau
We present a practical framework to prove, in a simple way, two-terms asymptotic expansions for Fourier integrals $$ {\mathcal I}(t) = \int_{\mathbb R}({\rm e}^{itϕ(x)}-1) {\rm d}…
Two arithmetic applications of perturbations of composition operators
Sandro Bettin, Sary Drappeau
We estimate the spectral radius of perturbations of a particular family of composition operators, in a setting where the usual choices of norms do not account for the typical size…
Averages of long Dirichlet polynomials
Sandro Bettin, J. Brian Conrey
We consider the asymptotic behavior of the mean square of truncations of the Dirichlet series of . We discuss the connections of this problem with that of the variance of t…
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…