Nancy-Metz number theory seminar - Institut Élie Cartan de Lorraine

Upcoming presentations

On real zeros of the first derivative of quadratic Dirichlet $L$-functions

Catégorie d'évènement : Séminaire de Théorie des Nombres de Nancy-Metz Date/heure : 27 November 2025 14:30-15:30 Lieu : Salle de conférences Nancy Oratrice ou orateur : Kunjakanan Nath (IECL) Résumé :

One of the central topics in number theory is the study of $L$-functions and the distribution of their zeros. For example, the celebrated Prime Number Theorem is equivalent to the fact that the Riemann zeta function $\zeta(s)$ does not vanish on the line $\text{Re}(s)=1$. In this talk, we will focus on quadratic Dirichlet $L$-functions: in particular, the real zeros of the derivative of quadratic Dirichlet $L$-functions $L^\prime (s, \chi_d)$, where $d$ ranges over fundamental discriminants. Baker and Montgomery conjectured that there are $\asymp \log \log |d|$ real zeros of $L^\prime(s, \chi_d)$ in the interval $[1/2, 1]$ for almost all fundamental discriminants $d$. We will highlight some recent exciting progress that comes close to proving this conjecture and then outline the proof, which is based on ideas coming from analytic and probabilistic number theory. This is based on recent joint work with Youness Lamzouri.

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Upcoming presentations

On real zeros of the first derivative of quadratic Dirichlet $L$-functions

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Past presentations

Stability of polynomials modulo primes

Sous-ensembles de réels ou du cercle de petite somme

Les problèmes de Goldbach et les zéros de la fonctions zeta de Riemann

Moyennes des root numbers de familles de courbes elliptiques

Discrete bilinear Radon transforms along arithmetic functions with many common values

La théorie de Ramsey arithmétique et les nombres premiers

Complex Moments and the distribution of Values of L(1,Ï‡D) over Function Fields with Applications to Class Numbers

Sur la complexité de familles d'ensembles pseudo-aléatoires

Chemins de Kloosterman de module une puissance d'un nombre premier

La répartition du maximum des sommes partielles de sommes d'exponentielles