S. Drappeau

activity

20132026

most citedSums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method

29 citations · 79 across the 18 of their papers we have counts for

collaborators

22 papers

math.NT2026

Computing sieve integrals using LattE, and the density of integers with a localized divisor

Sary Drappeau, Adrien Mounier

We consider the problem of estimating numerically integrals of the shape $\int_{P} \frac{d t}{t _{1} \dots t _{k}}$ where $P \in R_{> 0}^{k}$ is a convex polytope, $t=(t_1,\dots…

math.NT2024

Exponential sums over integers without large prime divisors

Sary Drappeau, Igor E. Shparlinski

We obtain a new bound on exponential sums over integers without large prime divisors, improving that of Fouvry and Tenenbaum (1991). For a fixed integer $ν \neq = 0$ , we also obtain ne…

math.NT2022★ 1 cited

On quantum modular forms of non-zero weights

Sandro Bettin, Sary Drappeau

We study functions $f$ on $Q$ which statisfy a ``quantum modularity'' relation of the shape $f (x + 1) = f (x), f (x) - ∣ x ∣^{- k} f (- 1/ x) = h (x)$ where $h:\mathbb R_{\ne…

math.NT2022

A modular analogue of a problem of Vinogradov

Ratnadeep Acharya, Sary Drappeau, Satadal Ganguly +1

Given a primitive, non-CM, holomorphic cusp form $f$ with normalized Fourier coefficients $a (n)$ and given an interval $I \subset [- 2, 2]$ , we study the least prime $p$ such that $a…

math.NT2022

Central values of additive twists of Maaß forms $L$ -functions

Sary Drappeau, Asbjørn Christian Nordentoft

In the present paper we study the central values of additive twists of Maaß forms $L$ -series. In the case of the modular group, we show that the additive twists (when averaged over…

math.NT2020

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}…

math.NT2020

The first moment of primes in arithmetic progressions: Beyond the Siegel-Walfisz range

Sary Drappeau, Daniel Fiorilli

We investigate the first moment of primes in progressions $q \leq x / N (q, a) = 1 \sum (ψ (x; q, a) - \frac{x}{φ ( q )})$ as $x, N \to \infty$ . We show unconditio…

math.NT2020

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…

math.NT2020★ 9 cited

One-level density estimates for Dirichlet L-functions with extended support

Sary Drappeau, Kyle Pratt, Maksym Radziwiłł

We estimate the $1$ -level density of low-lying zeros of $L (s, χ)$ with $χ$ ranging over primitive Dirichlet characters of conductor $\in [Q /2, Q]$ and for test functions whose Fourie…

math.NT2020

The Thue-Morse and Rudin-Shapiro sequences at primes in principal number fields

Sary Drappeau, Gautier Hanna

We consider a numeration system in the ring of integers $O_{K}$ of a number field, which we assume to be principal. We prove that the property of being a prime in ${\mathc…

math.NT2019

Modularity and value distribution of quantum invariants of hyperbolic knots

Sandro Bettin, Sary Drappeau

We obtain an exact modularity relation for the $q$ -Pochhammer symbol. Using this formula, we show that Zagier's modularity conjecture for a knot $K$ essentially reduces to the arit…

math.NT2019★ 8 cited

Partial sums of the cotangent function

Sandro Bettin, Sary Drappeau

Nous prouvons l'existence de formules de réciprocité pour des sommes de la forme $\sum_{m = 1}^{k - 1} f (\frac{m}{k}) cot (π \frac{mh}{k})$ , où $f$ est une fonction $C^{1}$ par morceaux, qui…

math.NT2019

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 $(0, 1]$ or…

math.NT2018★ 10 cited

Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions

Sary Drappeau, Berke Topacogullari

Given a multiplicative function $f$ which is periodic over the primes, we obtain a full asymptotic expansion for the shifted convolution sum $\sum_{∣ h ∣ < n \leq x} f (n) τ (n - h)$ , where…

math.NT2018★ 5 cited

Sign changes of Kloosterman sums and exceptional characters

Sary Drappeau, James Maynard

We prove that the existence of exceptional real zeroes of Dirichlet $L$ -functions would lead to cancellations in the sum $\sum_{p\leq x} \Kl(1, p)$ of Kloosterman sums over primes,…

math.NT2017

Exponential sums with automatic sequences

Sary Drappeau, Clemens Müllner

We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_{q} (f (n))$ , where $f$ is a rational fraction, in the Pólya-Vinogradov range. This a…

math.NT2017★ 1 cited

Statistical distribution of the Stern sequence

Sandro Bettin, Sary Drappeau, Lukas Spiegelhofer

We prove that the Stern diatomic sequence is asymptotically distributed according to a normal law, on a logarithmic scale. This is obtained by studying complex moments, and the ana…

math.NT2017★ 8 cited

Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$ -barrier

Sary Drappeau, Andrew Granville, Xuancheng Shao

We show that smooth-supported multiplicative functions $f$ are well-distributed in arithmetic progressions $a_{1} a_{2}^{- 1} (mod q)$ on average over moduli $q \leq x^{3/5 - ε}$ …

math.NT2016★ 4 cited

Weyl sums, mean value estimates, and Waring's problem with friable numbers

Sary Drappeau, Xuancheng Shao

In this paper we study Weyl sums over friable integers (more precisely $y$ -friable integers up to $x$ when $y = (lo g x)^{C}$ for a large constant $C$ ). In particular, we obtain an a…

math.NT2015★ 3 cited

On the average distribution of divisors of friable numbers

Sary Drappeau

A number is said to be $y$ -friable if it has no prime factor greater than $y$ . In this paper, we prove a central limit theorem on average for the distribution of divisors of $y$ -fr…

math.NT2015★ 29 cited

Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method

Sary Drappeau

We prove a bound for quintilinear sums of Kloosterman sums, with congruence conditions on the "smooth" summation variables. This generalizes classical work of Deshouillers and Iwan…

math.NT2013★ 1 cited

Propriétés multiplicatives des entiers friables translatés

Sary Drappeau

An integer is said to be $y$ -friable if its greatest prime factor P(n) is less than $y$ . In this paper, we study numbers of the shape $n - 1$ when $P (n) \leq y$ and $n \leq x$ . One exp…

Computing sieve integrals using LattE, and the density of integers with a localized divisor

Exponential sums over integers without large prime divisors

On quantum modular forms of non-zero weights

A modular analogue of a problem of Vinogradov

Central values of additive twists of Maaß forms L-functions

Effective estimation of some oscillatory integrals related to infinitely divisible distributions

The first moment of primes in arithmetic progressions: Beyond the Siegel-Walfisz range

Two arithmetic applications of perturbations of composition operators

One-level density estimates for Dirichlet L-functions with extended support

The Thue-Morse and Rudin-Shapiro sequences at primes in principal number fields

Modularity and value distribution of quantum invariants of hyperbolic knots

Partial sums of the cotangent function

Limit laws for rational continued fractions and value distribution of quantum modular forms

Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions

Sign changes of Kloosterman sums and exceptional characters

Exponential sums with automatic sequences

Statistical distribution of the Stern sequence

Smooth-supported multiplicative functions in arithmetic progressions beyond the x1/2-barrier

Weyl sums, mean value estimates, and Waring's problem with friable numbers

On the average distribution of divisors of friable numbers

Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method

Propriétés multiplicatives des entiers friables translatés

Central values of additive twists of Maaß forms $L$ -functions

Smooth-supported multiplicative functions in arithmetic progressions beyond the $x^{1/2}$ -barrier