Positions & Contact
Current position (April 2025–February 2026): Teaching and research fellow (ATER), University of Bordeaux
Future position (March 2026–August 2026): Postdoctoral researcher, Max Planck Institute for Mathematics (MPIM), Bonn.
Email: mounir.hayani[at]math[dot]u-bordeaux[dot]fr
About me
I am a postdoctoral researcher in analytic number theory at the University of Bordeaux. I completed my PhD in 2025 under the supervision of Florent Jouve and Daniel Fiorilli. My thesis, entitled Probabilistic distribution of prime numbers and ideals: Hooley's conjecture and Chebyshev's bias, studies how zeros of L-functions influence oscillations in the prime number theorem in arithmetic progressions as well as in the Chebotarev density theorem.
My work combines tools from analytic number theory, probability, and Galois theory to understand biases in the distribution of primes and prime ideals.
Research interests
- Chebyshev’s bias and prime / prime ideal races in number fields
- Oscillations in the Chebotarev density theorem and Galois group structure
- Moments of primes in arithmetic progressions
- Analytic and probabilistic aspects of Dirichlet and Artin L-functions
Publications and preprints
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Disproving a weaker form of Hooley's conjecture.
Bulletin des Sciences Mathématiques, Vol. 199 (2025), 25 pages. Preprint: arXiv:2407.01045. -
On the influence of the Galois group structure on the Chebyshev's bias in number fields.
Bulletin de la Société Mathématique de France, Vol. 153, No. 3 (2025), pp. 793–829. Preprint: arXiv:2404.06804.
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Prime ideal races with several competitors.
With A. Bailleul, submitted, 47 pages. Preprint: arXiv:2508.04087.
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Skewes numbers in prime number races.
With A. Bailleul and T. Untrau.
Teaching
- Mathematical Tools – exercise sessions (1st-year undergraduate); basic real analysis and foundations of calculus.
- Advanced Mathematics – exercise sessions (1st-year undergraduate); elementary number theory and analytic properties of real numbers.
- Algebraic Structures – exercise sessions (2nd-year undergraduate); groups, rings, and fields.
- Calculus in Several Variables – exercise sessions (2nd-year undergraduate); normed vector spaces and differentiable functions.
- Mathematics for Computer Science – exercise sessions (1st-year undergraduate); logic, sets, and basic algorithmics.
- Advanced Mathematics – lectures and exercise sessions (1st-year undergraduate); elementary number theory and analytic properties of real numbers.
Invited talks
- 33rd Journées Arithmétiques – Disproving a weaker form of Hooley's conjecture, Luxembourg, July 2025.
- Journées arithmétiques de Meknès – Extreme Chebyshev's bias in number fields, Meknès, April 2025.
- Séminaire ADA, Université du Littoral Côte d'Opale – Characterization of extreme cases of Chebyshev's bias in number fields, Calais, April 2025.
- Comparative Number Theory Symposium, UBC – The influence of the Galois group on Chebyshev's bias, Vancouver, June 2024.
- Analytic and Elementary Number Theory Meetings, IHP – Unconditional Chebyshev biases in number fields, Paris, June 2024.
- Lambda Seminar, Université de Bordeaux – Prime number races, Bordeaux, March 2024.