Rod2ik 🇪🇺 🇨🇵 🇪🇸 🇨🇱 🇺🇦 🇨🇦 🇬🇱☮🕊️Une avancée notable vers la résolution de l' #hypothèse de #Riemann .
Poir cela, #LarryGuth et #JamesMaynard utilisent des #polynômes de #Dirichlet et une meilleure borne de leurs zéros.
Référence : https://arxiv.org/abs/2405.20552
New large value estimates for Dirichlet polynomials
We prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length $N$ taking values of size close to $N^{3/4}$, which is the critical situation for several estimates in analytic number theory connected to prime numbers and the Riemann zeta function. As a consequence, we deduce a zero density estimate $N(σ,T)\le T^{30(1-σ)/13+o(1)}$ and asymptotics for primes in short intervals of length $x^{17/30+o(1)}$.