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

Groupe de Travail : Sommes de caractères de Dirichlet et applications (1)

Sur les plus grands facteurs premiers d'entiers consécutifs

Congruent numbers and ternary quadratic forms

Intersection d'une forme diagonale et d'un hyperplan : points rationnels et solutions p-adiques

Variations on a problem of Romanov

Implicit Function Theorem for Formal Power Series

Transcendence of $L(1,chi_s)/Pi$ and automata

Correlations of multiplicative functions

Moments of arithmetical sequences

On the density of shifted primes with large prime factors