LAMZOURI Youness

Position Full professor
Teaching department
Faculté des Sciences et Technologies
Research group Analysis and Number Theory
Research fields

Analytic Number Theory

Keywords
  • 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
Mail

IECL – Site de Nancy
Faculté des sciences et Technologies
Campus, Boulevard des Aiguillettes
54506 Vandœuvre-lès-Nancy

Email youness.lamzouri@univ-lorraine.fr
Phone number 03 73 74 54 47
Office 402

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:

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:

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:

Awards and Honours:

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.