Number Theory Seminar

Anup Dixit, Queen's University

"On Ihara's conjecture and the localized Erdos-Kac theorem"

As a natural generalization of the Euler-Mascheroni constant $\gamma$, Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to a number field $K$. He conjectured that for cyclotomic fields $\mathbb{Q}(\zeta_n)$, this constant is always positive. In this talk, we will discuss a connection of this conjecture with the number of small prime factors of $p-1$, for primes $p$. Motivated by this, we also establish a localized Erdos-Kac type theorem in this context.

MC 5417