Research

  I am interested in diverse aspects of number theory (analytic, algebraic, combinatorial, probabilistic) and its applications (cryptography, coding theory) as well as related fields like additive combinatorics, ergodic theory or finite fields.  

 More precisely, I am specialized in analytic and probabilistic methods and enjoy working on the following topics: L-functions, zeta functions of number fields, character and exponential sums, GCD sums, Dirichlet polynomials, prime numbers, friable numbers, sieve methods, multiplicative functions, distribution of sequences in arithmetic progressions.  I am also interested in applications in metric Diophantine approximation and uniform distribution.

Publications :

(28) Sign changes of short character sums and real zeros of Fekete polynomials (with O. Klurman and Y. Lamzouri), preprint.

(27)  Moments and non-vanishing of L-functions over subgroups (with I. E. Shparlinski), preprint.

(26)  L_q norms and Mahler measure of Fekete polynomials (with O. Klurman and  Y. Lamzouri), preprint.

(25) Pointwise and correlation bounds on Dedekind sums over small subgroups (with B. Borda and I. E. Shparlinski), to appear in Research in Number Theory.

(24)  Mean square values of L- functions over subgroups for non primitive characters, Dedekind sums and bounds on relative class numbers (with S. Louboutin), to appear in Canadian Journal of Mathematics, doi:10.4153/S0008414X2300010X 

(23) Additive energy and a large sieve inequality for sparse sequences  (with R. C. Baker and I. E. Shparlinski),  Mathematika, 2022, 362-399.

(22) Difference sets and the metric theory of minimal gaps (with C. Aistleitner and D. El-Baz),  IMRN, https://doi.org/10.1093/imrn/rnab354.

(21) Large sieve estimate for multivariate polynomial moduli and applications (with K. Halupczok),  Monatshefte für Mathematik 197 (2022), 463-478.

(20) A pair correlation problem, and counting lattice points with the zeta function (with C. Aistleitner and D. El-Baz),  Geometric and Functional Analysis  31 (GAFA),483-512.

(19) Small Gal sums and applications (with R. de la Bretèche and G. Tenenbaum), Journal of the London Mathematical Society (2021), Volume 103 (1), 336-352.

(18) A new large sieve inequality for power moduli,  Acta Arithmetica 197 (2021), 207-211.

(17) Second moment of Dirichlet L- functions, character sums over subgroups and upper bounds on relative class numbers (with S. Louboutin), Quarterly Journal of Mathematics 72 (2021), 1379-1399.

(16) Smooth squarefree and square-full integers in arithmetic progressions (with I. E. Shparlinski and K. H. Yau), Mathematika, Volume 66 (2020), no. 1, 56--70.

(15) Polynomial products modulo primes and applications (with O. Klurman), Monatshefte für Mathematik, 191(3), 577-593. 

(14) The maximum size of short character sums,  The Ramanujan Journal, 53, 27-38 (2020).

(13) On Large values of L(\sigma,\chi) (with C. Aistleitner, K. Mahatab and A. Peyrot), Quarterly Journal of Mathematics, Volume 70 (2019), no. 3, 831--848.  

(12) Extreme values of the Riemann zeta function on the 1-line (with C. Aistleitner and K. Mahatab), International Mathematical Research Notices, IMRN, Volume 2019 (2019), no. 22, 6924--6932. 

(11) On smooth square-free numbers in arithmetic progressions (with I. E. Shparlinski), J. London Math. Soc., 101: 1041-1067, 2020. 

(10) The Duffin-Schaeffer conjecture with extra divergence (with C. Aistleitner, T. Lachmann, N. Technau and A. Zafeiropoulous), Advances in Mathematics, Volume 356, 2019.

(9) On the minimal number of small elements generating prime fields, Bull. Aust. Math. Soc. 96 (2017), no. 2, 177--184.

(8) Square-full primitive roots (with T. Trudgian), Int. J. Number Theory 14 (2018), no. 4,  1013–1021.

(7) Shifted moments of L-functions and moments of theta functions, Mathematika, Volume 63 (2017), no. 1, 196-212.

(6) Upper and lower bounds for higher moments of theta functions (with I. E. Shparlinski), Quarterly Journal of Mathematics, Volume 67 (2016), no. 1, 53--73.

(5) Distribution of factorials modulo p (with O. Klurman), Journal de Théorie des Nombres de Bordeaux 29 (2017), no. 1, 169-177.

(4) Congruences with intervals and subgroups modulo a prime (with I. E. Shparlinski), Michigan Math. J , Volume 64 (2015), no. 3, 655-672.

(3) Character sums over squarefree and squarefull numbers, Arch. Math. (Basel) 102 (2014), no. 6, 555-563.

(2) On positive real zeros of theta and L-functions associated with real, even and primitive

characters (with Stephane Louboutin), Publ. Math. Debrecen 83/4 (2013), 643-665.

(1) The second and fourth moments of theta functions at their central point (with Stephane

Louboutin), J. Number Theory 133 (2013), no. 4, 1186-1193.

Documents not intended for publication: 

(1) Non vanishing of theta functions and sets of small multiplicative energy, superseded by the publication (17) above.

Thesis :

Moments des fonctions thêta, soutenue le 12 décembre 2013 à l'Institut de Mathématiques de Luminy (IML).