Number Theory Seminar

Peter KoymansETH Zurich
Spins, Galois representations and a question of Ramakrishna

Friday, March 15, 2024 - 2:30pm

Let $E$ be the elliptic curve $y^2 = x^3 - x$, and define $a_p(E) = p + 1 - |E(\mathbb{F}_p)|$. Ramakrishna asked if there are infinitely many primes $p \equiv 1 \bmod 3$ such that $a_p(E)$ is a cubic residue modulo $p$. We shall show how this question is intimately related to so-called "spins of prime ideals", and we shall overview the main results and ideas on obtaining estimates for spins. We will then use this theory to obtain the asymptotic density of the primes $p$ in Ramakrishna’s question.

This talk will be given via Zoom ( )
We will gather to watch the talk in the 3rd floor conference room.