Faculté des Sciences et Technologies
Théorie analytique des nombres / Analytic Number Theory
- Character sums and exponential sums
- The Riemann zeta function and L-functions
- The distribution of prime numbers
- Additive and multiplicative functions
- Class numbers of quadratic fields
- Random multiplicative functions
IECL – Site de Nancy
Faculté des sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy
I am a Professor of Mathematics at the Institut Elie Cartan de Lorraine (IECL) of the Université de Lorraine in Nancy, France.
I am also a Junior Member (laureate of a Fundamental Chair) of the Institut Universitaire de France (IUF).
Before joining the Institut Elie Cartan de Lorraine in 2018, I was an Associate Professor at York University in Toronto, Canada, where I remained from 2012 to 2018. From 2009 to 2012, I had postdoctoral positions at the Institute for Advanced Study in Princeton, USA, and the University of Illinois at Urbana-Champaign, Urbana, USA.
I received my PhD in 2009 from the University of Montreal under the supervision of Andrew Granville. My thesis « Sur la distribution des valeurs de la fonction zêta de Riemann et des fonctions L au bord de la bande critique » has received the 2011 Blair Spearman Doctoral Prize from the Canadian Mathematical Society.
My research interests are in analytic and probabilistic number theory. I am interested in various questions concerning character sums and exponential sums, the theory of the Riemann zeta function and L-functions, prime number races, class numbers of quadratic fields, Fourier coefficients of modular forms, as well as random multiplicative functions.
Currently, I am on the editorial boards of the following journals:
- Bulletin et Mémoires de la société mathématique de France.
- Journal de Théorie des Nombres de Bordeaux (JTNB).
I co-organize the Nancy-Metz Number Theory Seminar, and I am the organizer of the Mathematics Colloquium at the IECL, Nancy.
Personal:
- Born in 1983.
- Citizenship : Canada and Morocco.
Academic positions:
- 2023-2028: Junior Member of the Institut Universitaire de France
- 2018-present: Professor, Université de Lorraine, Nancy, France (promoted to 1st class in 2024)
- 2016-2020: Associate Professor, York University, Toronto, Canada (on leave during 2018-2020)
- 2012-2016: Assistant Professor, York University, Toronto, Canada
- 2010-2012: J. L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign, Urbana, USA
- 2009-2010: Member, Institute for Advanced Study, Princeton, USA
Visiting positions :
- 10/2024-01/2025: Simons-CRM Professor, Centre de Recherches Mathématiques, Montréal, Canada.
- 09/2022-03/2023: Délégation CNRS, IRL CNRS-CRM, Centre de Recherches Mathématiques, Montréal, Canada.
- 05/2017-08/2017: Poste Rouge du CNRS, Université de Lorraine.
Education:
- Ph.D. in Mathematics, Université de Montréal, Canada, 2009. Advisor: Andrew Granville.
- B.Sc. in Pure Mathematics, Université de Montréal, Canada, 2004.
Awards and Honours:
- Junior Chair, Institut Universitaire de France (2023-2028).
- CMS Blair Spearman Doctoral prize, Canadian Mathematical Society, 2011.
- NSERC Postdoctoral Fellowship, Natural Sciences and Engineering Research Council of Canada, 2009-2011.
- Alexander Graham Bell Canada Graduate Scholarship, NSERC, 2006-2009.
- Carl Herz Scholar, Institut des Sciences Mathématiques du Québec (ISM), 2006.
- Jean-Maranda Award, Université de Montréal, 2004.
- Maurice-L’abbé Award, Université de Montréal, 2003.
- Gold Medal, Moroccan Mathematical Olympiad, 1998.
46. (With Kunjakanan Nath) The distribution of the maximum of cubic character sums. Submitted, 32 pages. [arXiv]
45. On the distribution of the error terms in the divisor and circle problems. Submitted, 19 pages. [arXiv]
44. (With Oleksiy Klurman and March Munsch) Sign changes of short character sums and real zeros of Fekete polynomials. Submitted, 45 pages. [arXiv]
43. (With Oleksiy Klurman and March Munsch) Lq norms and Mahler measure of Fekete polynomials. Submitted, 24 pages. [arXiv]
42. An effective Linear Independence conjecture for the zeros of the Riemann zeta function and applications. To appear in the Springer volume: « Essays in Analytic Number Theory: In Honor of Helmut Maier’s 70th Birthday », 19 pages. [arXiv]
41. The distribution of large quadratic character sums and applications. To appear in Algebra and Number Theory, 43 pages. [arXiv]
40. (With Ayesha Hussain) The limiting distribution of Legendre paths. Journal de l’École polytechnique — Mathématiques, Tome 11 (2024), pp. 589–611. [arXiv]
39. (With Y. Lee) The number of zeros of linear combinations of L-functions near the critical line. Journal d’Analyse Mathématique, Vol. 152 (2024), no. 2, 669–727. [arXiv]
38. (With A. Languasco) Small values of $|L’⁄L(1, χ)|$. Experimental Mathematics, Vol. 32 (2023), no.2, 362–377. [arXiv]
37. (with M. Gerspach) Low pseudomoments of Euler products. The Quarterly Journal of Mathematics, Vol. 73 (2022), no. 2, 517–537. [arXiv]
36. (With Alexander P. Mangerel) Large odd order character sums and improvements of the Pólya-Vinogradov inequality. Transactions of the American Mathematical Society, Vol. 75 (2022), no. 6, 3759–3793. [arXiv]
35. (with A. Granville) Large deviations of sums of random variables. Lithuanian Mathematical Journal (Kubilius Centenary issue), Vol. 61 (2021), no. 3, 345–372. [arXiv]
34. Zeros of the Epstein zeta function to the right of the critical line. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 171 (2021), no. 2, 265–276. [arXiv]
33. (With P. Autissier and D. Bonolis) The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica, Vol. 157 (2021), no. 7, 1610–1651. [arXiv]
32. On the distribution of the maximum of cubic exponential sums. Journal of the Institute of Mathematics of Jussieu, Vol. 19 (2020), no. 4, 1259-1286. [arXiv]
31. (With Stephen Lester and Maksym Radziwill) Discrepancy bounds for the distribution of the Riemann zeta function and applications. Journal d’Analyse Mathématique, Vol. 139 (2019), no. 2, 453-494. [arXiv]
30. (With Bruno Martin) On the race between primes with an odd versus an even sum of the last $k$ binary digits. Functiones et Approximatio Commentarii Mathematici, Vol. 61 (2019), no. 1, 7-25.
29. (With Kevin Ford and Adam Harper) Extreme biases in prime number races with many contestants. Mathematishe Annalen, Vol. 374 (2019), no. 1-2, 517-551. [arXiv]
28. Large sums of Hecke eigenvalues of holomorphic cusp forms. Forum Mathematicum, Vol. 31 (2019), no. 2, 403-417. [arXiv]
27. (With Stephen Lester and Maksym Radziwill) An effective universality theorem for the Riemann zeta function. Commentarii Mathematici Helvetici, Vol. 93 (2018), no. 4, 709–736. [arXiv]
26. (With Alex Dahl) The distribution of class numbers in a special family of real quadratic fields. Transactions of the American Mathematical Society, Vol. 370 (2018), no. 9, 6331-6356. [arXiv]
25. (With Régis de la Bretèche and Gérald Tenenbaum) Inégalité de Turán-Kubilius friable et indépendance asymptotique. Acta Arithmetica, Vol. 183 (2018), no. 2, 191-199. [arXiv]
24. (With Adam Harper) Orderings of weakly correlated random variables, and prime number races with many contestants. Probability Theory and Related Fields, Vol. 170 (2018), no. 3-4, 961-1010. [arXiv]
23. The number of imaginary quadratic fields with prime discriminant and class number up to $H$. The Quarterly Journal of Mathematics, Vol. 68 (2017), no. 4, 1379-1393. [arXiv]
22. On the average of the number of imaginary quadratic fields with a given class number. The Ramanujan Journal, Vol. 44 (2017), no. 2, 411-416. [arXiv]
21. Large moments and extreme values of class numbers of indefinite binary quadratic forms. Mathematika, Vol. 63 (2017), no. 2, 564-586. [arXiv]
20. Large values of $L(1, \chi)$ for $k$-th order characters $\chi$, and applications to character sums. Mathematika, Vol. 63 (2017), no. 1, 53-71. [arXiv]
19. A bias in Mertens’s product formula. International Journal of Number Theory, Vol. 12 (2016), no. 1, 97-109. [arXiv]
18. Extreme values of class numbers of real quadratic fields. International Mathematics Research Notices, IMRN 2015, no. 22, 11847-11860. [arXiv]
17. The distribution of Euler-Kronecker constants of quadratic fields. Journal of Mathematical Analysis and Applications, Vol. 432 (2015), no. 2, 632-653. [arXiv]
16. (With Xiannan Li and Kannan Soundararajan) Conditional bounds for the least quadratic non-residue and related problems. Mathematics of Computation, Vol. 84 (2015), no. 295, 2391-2412. [arXiv]
15. (With Leo Goldmakher) Large even order character sums. Proceedings of the American Mathematical Society, Vol. 142 (2014), 2609-2614. [arXiv]
14. (With Kevin Ford and Sergei Konyagin) The prime number race and zeros of Dirichlet L-functions off the critical line: Part III. Quarterly Journal of Mathematics, Vol. 64 (2013), no. 4, 1091-1098. [arXiv]
13. The distribution of short character sums. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 155 (2013), no. 2, 207-218. [arXiv]
12. Prime number races with three or more competitors. Mathematische Annalen, Vol. 356 (2013), no. 3, 1117-1162. [arXiv]
11. (With Leo Goldmakher) Lower bounds on odd order character sums. International Mathematics Research Notices, IMRN (2012), no. 21, 5006-5013. [arXiv]
10. The Shanks-Rényi prime number race with many contestants. Mathematical Research Letters, Vol. 19 (2012), no. 03, 649-666. [arXiv]
9. (With Alexandru Zaharescu) Randomness of character sums modulo $m$. Journal of Number Theory, Vol. 132 (2012), no. 12, 2779-2792. [arXiv]
8. Large deviations of the limiting distribution in the Shanks-Rényi prime number race. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 153 (2012), 147-166. [arXiv]
7. On the distribution of extreme values of zeta and L-functions in the strip $1/2<\sigma<1$. International Mathematics Research Notices, IMRN 2011, no. 23, 5449-5503. [arXiv]
6. (With M. Tip Phaovibul and Alexandru Zaharescu) On the distribution of the partial sum of Euler’s totient function in residue classes. Colloquium Mathematicum, Vol. 123 (2011), 115-127.
5. Extreme values of $\arg L(1, \chi)$. Acta Arithmetica, Vol. 146 (2011), 335-354. [arXiv]
4. Distribution of values of L-functions at the edge of the critical strip. Proceedings of the London Mathematical Society, (3) 100 (2010), no. 3, 835-863. [arXiv]
3. The two dimensional distribution of values of $\zeta(1+it)$. International Mathematics Research Notices, IMRN (2008) Vol. 2008, article ID rnn106, 48 pp. [arXiv]
2. On the number of linear forms in logarithms. Journal of Number Theory, Vol. 125 (2007), 247-253. [arXiv]
1. Smooth values of the iterates of the Euler Phi function. Canadian Journal of Mathematics, Vol. 59, No. 1 (2007), 127-147. [arXiv]
Doctoral students:
- Amine Iggidr (co-supervised with Thomas Stoll). Université de Lorraine (2024-present).
- Kilian Lebreton. Université de Lorraine (2024-present).
- Mustapha Talibi (co-supervised with Abdelaziz Raouj). Université Cadi-Ayyad de Marrakech (2024-present).
- Jérémy Dousselin. Université de Lorraine (2021-present).
- Youssef Sedrati (co-supervised with Manfred Madritsch). Université de Lorraine (2019-2023). Currently: Lecturer at CESI Engineering School, Lyon.
- Allysa Lumley. York University (2015-2019). Currently: Assistant Professor (Teaching Stream) at York University.
Postdoctoral Researchers:
- Kunjakanan Nath. Université de Lorraine (2024-2026).
- Alexander Dahl. York University (2015-2017). Currently: AI Software Developer at Smile Digital Health, Toronto.
Master students:
- Amine Iggidr (Ecole Polytechnique). Université de Lorraine, 2024.
- Kilian Lebreton (ENS de Rennes). Université de Lorraine, 2024.
- Jérémy Dousselin (ENS de Lyon). Université de Lorraine, 2021.
- Émile Séguret (ENS Cachan), co-supervised with with Cécile Dartyge. Université de Lorraine, 2020.
- Martin Scotti (Université de Paris 6). Université de Lorraine, 2020.
- Youssef Sedrati (Université de Bordeaux). Université de Lorraine, 2019.
- Samuel Dupuis. York University, 2017–2018.
- Comparative Prime Number Theory Symposium, UBC, Vancouver, Canada. June 17-21, 2024.
- Séminaire COOL, Institut Henri Poincaré, Paris, France. October 18, 2024.
- Research visit to the CRM, supported by a Simons-CRM Professor position, Centre de Recherches Mathématiques, Montréal, Canada. October 30th 2024 to January 15, 2025.
- Prime numbers and arithmetic randomness, CIRM, Marseille, France. June 23-27, 2025.